First "Mahayana" can be very broad. It is usual to divide Buddhism into two broad categories: Mahayana and Theravada. Thus, Vajrayana, Zen/Chan, and Jodo Shinshu are all part of Mahayana, Zen and Jodo Shinshu being schools, and Vajrayana a broad category covering tantric Buddhism.

Chinese Mahayana Buddhism, and its offshoots in Korea, Japan, and Vietnam, originated in Central Asia. Buddhism travelled north from India, and into Sogdia (upper Transoxiana, centred around cities such as Samarkand and Bukhara). From there, to China. Central Asian Buddhism was largely displaced by the spread of Islam, leaving traces, including very spectacular ones such as the Buddhas of Bamiyan, which stood for one and half millennia until their destruction by the Taliban in 2001. The Buddhism that emerged into China had been changed by its passage, and the distinctiveness of East Asian Mahayana is due to this evolution as Buddhism passed through Central Asia, as well as further evolution in China.

Buddhism in Japan has a long history, the early part of which isn't well known. The Nihon Shoki (AKA Nihongi) places the arrival of Buddhism (from Korea) in the mid-6th century. Not all of the early Japanese schools are considered Mahayana by all, with 2 of the main early 6 schools (all ultimately of Chinese origin) being labelled as "Hinayana" ("inferior vehicle", in contrast to "Mahayana", "great vehicle", with derogatory intent). Buddhism grew in Japan in the Heian Period, and new schools were introduced and developed, notably Tendai (Tiantai in China, literally "Heavenly Tower", but AKA the "Lotus School"). When Chan (AKA Zen) reached Japan at the end of the 12th century, it absorbed much from Tendai (both from Japanese Tendai and from Chinese Tiantai). The 13th century saw the arrival or development of the biggest schools of the future: Nichiren Buddhism developed from Tendai, and Pure Land Buddhism.

Simplifying (oversimplifying, even), we can contrast Zen and Pure Land Buddhism by Zen's focus on self-improvement and personal enlightenment, and Pure Land's belief in the inherent corruption of the world and salvation through faith, with rebirth in the Pure Land (i.e., Heaven). The Pure Land practice of seeking mindfulness of the Buddha through repetition of the name of Amitabha (AKA Amida Buddha) in prayer led to the alternative English name of Amidism. Self-improvement vs acceptance of a corrupt world with hope for a rebirth in the Pure Land as a result of faith may well have influenced the spread of these very different types of Buddhism among the upper classes and the peasantry, respectively.

Jodo Shinshu is a Pure Land school. When it began, it was criticised by other sects (including other Pure Land sects). First, they believed that the world was becoming increasingly degenerate and corrupt, and older paths to enlightenment and salvation were no longer effective. This was an at least implicit criticism of other schools. Its prioritisation of faith over ritual was also a criticism of other schools. Jodo Shinshu, and in particular Hongan-ji, grew spectacularly in the 15th century, which attracted attention from the great secular power players, such as Oda Nobunaga and Tokugawa Ieyasu, and other sects. Mt Hiei took military action against Honganj-ji, and Oda Nobunaga also did so. A Hongan-ji faction which supported Togugawa Ieyasu was rewarded by Ieyasu by recognition as an independent sect, with its own lands. This division is often described as an action by Ieyasu to limit the power of Hongan-ji by breaking it into distinct sects, and reducing the power of the non-supportive factions of Hongan-ji may well have been one of his motives.

The religious basis of the Ikko-Ikki was Hongan-ji, but (a) the leadership of Hongan-ji kept themselves distanced from the Ikko-Ikki, prominently repeating their rejection of violence, and (b) the Ikko-Ikki didn't obey the leadership of Hongan-ji. The Ikko-Ikki did have communist elements in their religious and political belief (as did comparable European politico-religious movements such as the Hussites and the Levellers).

The 16th century growth of Jodo Shinshu, especially of Hongan-ji, and the popular appeal of the sect, led to it being the biggest sect in modern Japan. This isn't due to some miraculous recovery after systematic suppression. Jodo Shinshu was suppressed in southern Kyushu in the mid-late 16th century, remaining banned there until the Meiji Restoration. This led to the underground Kakure Nenbutsu groups preserving Jodo Shinshu teachings there. However, this was only a localised suppression, and as noted above, some factions received official support from the Tokugawa government, thanks to well-timed support given to the Tokugawa in their climb to power.

Postscript: Shingon Buddhism is the biggest surviving Japanese tantric Buddhist school, and is part of Vajrayana. This comes from old Chinese roots, and owes little if anything to Tiberan Vajrayana. Tibetan Vajrayana Buddhism had its biggest pre-modern spread outside Tibet when the Mongol Empire adopted Tibetan Buddhism.

Further reading:

On the development of Jodo Shinshu: Dobbins, J. (1986), "From Inspiration to Institution. The Rise of Sectarian Identity in Jōdo Shinshū", Monumenta Nipponica 41(3), 331-343. https://doi.org/10.2307/2384681 https://www.jstor.org/stable/2384681