The two commonly overlap in China, but the same is not true in Japan. After the Manchu takeover of the Chinese central government, religion became very mixed. The Manchus, of course, were Mongolian/Tibetan Buddhists. I don't know too much about Chinese Buddhism in the 15th--19th centuries. When a new strand of Zen came to Japan in the 17th century, however, it did not achieve much popularity. The new school was the Obaku School, and the chief barrier to popularity was the way it mixed different kinds of Buddhist practice--specifically Zen and Pure Land. Everyone was expecting something purer and closer to the source, but what they got was a jumble.
This is nonsense- I think you're just pulling theories out of your back pocket. The mixing is just a natural expression of the Mahayana concept of "skillful means" (upaya). All Chinese Mahayana Buddhists accepted the same big canon of scriptures from India. All of these sutras were considered authoritative and taught by the Buddha, including not only the Lotus Sutra or the Flower Ornament Sutra but sutras advocating particular devotional practices like the Pure Land sutras or the sutra of Ksitigharbha Bodhisattva, and also a few lower-level tantras. All the schools of Mahayana Buddhism- Chan, Pure Land, Tiantai, etc., accept this canon.
The first purely Chinese school of Buddhism was the Tiantai school (Tendai in Japan) which tried to put forward a system for integrating this vast range of teachings and practices. The Buddha taught them all, so naturally they must fit together somehow. They took the Lotus Sutra as the highest sutra, but accepted that the varieties of seated meditation practices, and more devotionally oriented practices ike nian fo
, were all valid "skillful means" for bringing people to enlightenment, according to their dispositions. The Huayan school had a similar project, but centered on the Avatamsaka Sutra. Other sutras were deemed less central but nonetheless important and edifying.
Both of these schools arose centuries before any Manchu influence and then spread to Japan. Manchus had very little influence on the common religious life in China. Tibetan Buddhism remains rather "niche" among Chinese. Vajrayana practice in general is quite rare in Chinese Buddhism.
Tiantai spread to Japan as Tendai and was the mother sect of almost all the big-name Japanese Buddhist reformers- Dogen, Shinran, Nichiren, etc. And you want to claim that the integration of various Buddhist practices is a Manchu innovation?
Eventually Chan became the dominant sect in China, absorbing the other sects. Instead of wiping out their practices, though, it tended to integrate them more.
Everyone was expecting something purer and closer to the source, but what they got was a jumble.
"Purer"? Once again, everyone in the Mahayana accepts that the Buddha taught Pure Land, Chan, etc., so how is this a question of purity?
So you have to distinguish when you're talking about these schools which country you're referring to. Vietnam is another entirely different issue, for example.
Not very different at all. Vietnamese culture is profoundly influenced by China and Buddhism is no exception. Vietnamese Buddhism is just as "mixed" as Chinese Buddhism.
But the difference in some of the basic Buddhist texts is just as profound. For example, the Heart Sutra is chanted hundreds of thousands of times a day in Japanese temples in a version that is profoundly different than the one used in Chinese temples. It's not just the difference between short and long forms. The texts themselves differ profoundly in a few places. So in a very real sense Mahayana Buddhists are not using the same scriptures, and this affects the meaning of their core teachings.
???The Heart Sutra chanted in Japanese temples is just the Japanese pronunciation of the Chinese translation.