In Japan, it is said more than 300 varieties or 600 varieties can be identified which delivered from species or sub-species native in Japan which can be more or less 100, and the 10 most important ones are selected as basic species. From these natives, more than 200 or 500 cultivars could be developed. Therefore we can enjoy to watch variety of cherry or Sakura blossoms from very early spring to early summer, and some varieties bloom in autumn again. I am sometimes excited or sometimes relieved by watching cherry blossoms for enjoying good spring season. 日本語のページはこちらです。
These species or cultivars have many different characteristics such as flower color, petal styles, blooming time and so so.
A list of each variety in table is here (with picture), and list without pictures is here.
Please watch beautiful cherry blossom scene in Japan and explanation of cherry from my YouTube clips.
For classifying my pictures, I use web information such as Wikipedia or website of "The Flower Association of Japan" http://www.hananokai.or.jp/sakura-zukan/, as well as labels on trees. However, I am afraid I may misunderstand, since there are many similar varieties. Please allow me if you may find my misunderstanding, and please let me know so.
Biological name of cherry genus can be used Cerasus, mainly in Japan or Prunus, I mainly use Cerasus and abbreviation as C.
Cerasus jamasakura; Yamazakura

Yamazakura (C. jamasakura) , means mountain or hilly cherry, is one of the most important native species grown in mountain area as well as Oyamazakura (C. sargentii), Kasumizakura (C. leveilleana), Osimazakura (C. speciosa) and Kumanozakura (C. kumanoensis).
C. jamasakura is the most popular species among the 5 species above grown in mountain area, but it is observed wide variation of many characteristics in each plants such as flowering time, flower type, timing of first fresh leaves and flower, and color of flower and leaf, and so on, among species grown even in same area. C. jamazakura is an independent species but sometimes confusion of identification with C. sargentii and C. leveilleana and called as "Mountain cherry " in as same together.
There are many cultivated varieties or cultivars from this native species from ancient time and some cultivars could be difficult to identify original species. Some poplar cultivars known from this species are Kotohira and Ichihara-Toranoo.
C. sargentii; Sargent’s cherry (Oyama-zakura)

Sargent’s cherry (Oyama zakura) (C. sargentii) is grown in high altitude comparing with Yamazakura (C. jamasakura) in mainland Japan , Honsyu. However in Hokkaido, Northern Island, it is grown in low altitude, or plain. Color of petal is much darker pink than Yama-zakura or Kasumi-zakura (C. leveilleana) , therefore the species are sometime called Red-Yamazakura or Ezo-yamazakura (Ezo is former name of Hokkaido).
Varieties originated from this native species are Kenrokuen-kumagaya, original tree is planted in Kenrokuen, garden in Kanazawa or Oshusatozakura. Another popular variety is Accolade, which is much popular in Europe since it was developed in U.K.
C. leveilleana/C. verecunda; Kasumizakura

Kasumizakura (C. verecunda) is grown in higher altitude than C. jamasakura and has similar characteristics as C.jamasakura as sprouting flower and green leaf in same time (color of fresh leaf of C. jamasakura is usually reddish green). Since color of fresh leaf of Oshimazakura (C. speciosa) is same as Kasumizakura and is considered as island type (Izu islands) of Kasumizakura with very limited difference such as distinguished by presence of pubescence of petiole and peduncle.
Kasumizakura is considered as basis of many cultivars but cannot be identified clearly from Yamazakura or Oshimazakura. Some of varieties considered most likely from the Kasumizakura can be Sasabe-zakura or Benitamanishiki.
C. speciosa; Oshimazakura

Oshimazakura (C. speciosa) is considered as an island type of Kasumizakura (C. leveilleana/C. verecunda) and original tree is existing in a Oshima island in Izu islands and, this variety popularly known as parental lines of Someiyoshino or other many poplar varieties or cultivars, although Somisiyosino is classified as Edo-higan group, which is other parental line.
Oshimazakura has more whitish petal than Someiyoshino, blooming time is varied in individual plants and some early blooming variants can be seen. The flowers has good aroma and be used as rolling leaf for Sakura mochi, Sakura rice cake.
Wild plant is single white petals of mid time flowering, but some cultivars are produced as early blooming, called as Kanzaki-oshima or Yae-beni-oshima, pink double blooming one. And as of good smelled cultivated varieties, Gozanoma-nioi or Surugadai-nioi, nioi means good smell, are produced from this species.
C. kumanoensis; Kumanozakura

Kumanozakura (C. kumanoensis) is registered as new species in 2018, which grown in Kii-peninsular and classified as basic wild species in Japan. The Kumanozakura is darker pink and early blooming than Yamazakura (C. jamasakura) .
C. spachiana/ C. pendula; Edohigan

Edohigan (C. spachiara/ C. pendula) is a native species of Japan, and as the name (Edo is name of former Tokyo, and Azuma means eastern) suggests, it blooms in the plains of Tokyo and eastern Japan around the equinoctial week in spring, and blooms earlier than Somei-yoshino, the most popular cherry variety and decendant of this variety.
The flowers are light pink to white, with five single petals, and the flowers bloom before the leaves. It is known to be a very longivity among cherry blossoms along with Yamazakura, and it is said that the three giant cherry trees in Japan, Yamataka Jindai in Hokuto Yamanashi, more than 2,000years, Usuzumi in Neo Gifu, more than 1,500years and Miharu Takizakura in Fushima over 1,000year Japan are of this Edohigan group.
The flower has single pale pink petals, blooming faster than leaf such nature called as "Ubasakura"group.
Since it has many flowers without leaves on branch, it is used as mother plants of many cultivars, it is easy to distinguished by round shape of bottom of sepal. The varieties from this species are Komatsu otome, which considered as a very closed variety of Someiyoshino like direct brother, America, which is reproduced from a Someyoshino planted in USA, and Jindai-akbono, which is bred form the America and expected to become a popular variety as next generation of Someiyoshino. And as another popular variety is weeping variety called Yaebeni-shidare.
C. incisa; Mamezakura

As named as Mame-zakura (C, incisa), mame' s Japanese mean is small, this species has relatively low height of tree and small flowers and it blooms some days earlier than Someiyoshino. As original habitat area is around Mt. Fuji and Hakone area, the species sometimes called Fujizakura or Hakonezakura. Other species or sub-species grown in Kinki region as called Kinki mamezakura, is belongs this group.
The characteristics as low height is preferred as a garden tree and used as parent of some cultivars such as Umineko, popular variety in Europe or four seasons blooming variety Fuyuzakura. Also it is known as used for making varieties such as Okamezakura, Kohigan.
C. apetala; Chyoujizakura

Chyoujizakura (C. apetala) is one of the basic wild species of cherry and has small white to very pale pink petals and long and wide calyx tube. Since shape from side angle looks like clove flower or T-shape, this species is called Chyoujizakura or Clove cherry.
Cultivated varieties originated from the Choujizakura is known such as Takasago.
C. nipponica; Takanezakura

Takanezakura (C. nipponica) is a one of the basic wild species and grown in high mountain area. It blooms very late in early May and pale pink with darker in center circle. Chishima zakura (Kurile cherry), which is grown in East part Hokkaido is considered as variant of Takanezakura.
C. maximowiczii; Miyamazakura

Miyamazakura (C. maximowiczii) is grown in Japan from Hokkaido to Kyusyu, in high altitude in mountain and it blooms after complete appearance of leaves.
C. campanulata; Hikanzakura

Hikanzakura (C. campanulata) (or sometimes called Kanhizakura) is early blooming species with strong scarlet pink or red originated in Taiwan, we can enjoy varieties blooming early such from in February in Tokyo. Although it is not included in basic 10 wild species in Japan but introduced for producing many early blooming varieties. From its bell shape flower it has name of campanulata. It is said in Japan not opened fully but opened in Taiwan.
Popular varieties made from this species are Atamin-hayazaki, Kawadzuzakura, Okame-zakura, Youkou.
C. serrulata/ C. lannesiana; Satozakura

Satozakura (C. serrulata/ C. lannesiana), sato's Japanese mean is a village or town, so Satozakura means "cherry in town", which produced by crossing with many species or existing varieties, mainly from Oshimazakura (C. speciosa) and Yamazakura(C. jamasakura), Edohigan (C. spachiana/ C. pendula), Kasumizakura( C. leveilleana/C.verecunda) and Mamezakura(C. incisa).
History of Satozakura planted in a garden is back to Heian period, more than 1000 years ago, and from this time, many breeding methods have been used like artificial crossing and selection from natural crossing, mutant and so on. And then more than 200 varieties has been produced, and it is said contribution or influence by Oshimazakura seems to be very large.
Breeding is mainly focused on ornamental value, therefore, large number of petals including double petals or double of narrow petal, weeping branch or very large petals varieties has been preferred.
Color of flower also has many variation such as white, shallow pink, dark pink, scarlet, purple and yellow green also changing color by time after blooming. Many varieties blooming same time or later of Someiyoshino, some varieties has long blooming time.
Some of popular varieties with various characteristics include, Shirotae (white, double), Taihaku (white, large single), Ichiyou (pale pink, double), Fugenzou (pale pink, double), Baigoji-jyuzukake-zakura (pink, double of narrow petal), Kanzan (dark pink or scarlet, double), Yaemurasaki (purplish pink, double), Cyosyu- hizakura (purplish scarlet, semi double), Ukon ( yellow green, double) and Gyoikou ( yellow green, double).
C. pseudo-cerasus; Karamizakura

Karamizakura (C. pseudo-cerasus) is china origin and fruit is edible with sour taste. Currently commercial production of cherry in Japan is based on variety from sweet cherry, Seiyou-mizakura (Prunus avium), this species is mainly used for parent line for early blooming variety.
Varieties produced from this species are Tokaizakura, which is also known as Keiozakura for production of cut flowers, or Kobuku zakura, famous variety blooming spring and autumn.
Others

Some other species or varieties not listed above because of native area is far from Japan or not included in Cerasus bur near species to cherry species (usually classified as Prunus) are classified as others in below.
Wild Himalayan cherry (Cerasus cerasoides) is native in Himalayan region, Sweet cherry (Cerasus avium) native in Europe is planted mainly for cherry fruit production.
Some bush type Prunus close to cherry, native in China can be seen in Japan, Chinese bush cherry (Prunus glandulosa), (Japanese name: Niwa-zakura means garden cherry), and Japanese bush cherry (Cerasus japonica or Prunus japanica), (Japanese name: Niwa-ume means garden Japanese apricot). And Almond (Prunus dulcis) blooms similar pale pink five petals flowers in spring.
Other group near cheery native in Japan is a kind of bird cheery, which flower is not so eye-catching usually blooms after fresh leaves opened, such tree are Dog cherry(Prunus buergeriana), and Japanese bird cherry (Prunus grayana).
These species or cultivars have many different characteristics such as flower color, petal styles, blooming time ans so so. In a table below, you may find many varieties are classified by such characteristics or origins, and you can change order of line by clicking the top line of table.
A list of table of cherries with picture is here, and list without pictures is here.