Anemone is a genus that has been both variously split up and remerged in light of molecular data.
As usual, this is all initially confusing but ultimately, it should help elucidate evolutionary relationships.
The Fall-blooming Anemones are now in the genus Eriocapitella. This group is also known as the Japanese Anemone, but they are not native to Japan, though long-cultivated there. Eriocapitella is native to southern and southeastern Asia, China, Taiwan, and Sumatra.
A large group of small Woodland Anemones native to North America, British Isles, Eurasia, Taiwan, Sakhalin, and Japan is now placed in the genus Anemonoides. The well known tuberous perennial, the Grecian Windflower (Anemonoides blanda) is also in this group.
The Pasqueflowers have often been separated into the genus Pulsatilla, but recent treatments again include them within Anemone.
Likewise, the Liverleafs (Hepatica) and Knowltonia are other genera that may be once again included within Anemone.