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Touhou: Eastern Story. Popular. Made by ZUN. Has a female cast mostly. 6+ New characters in each game (excluding official spin-offs). Shooting games focused on slow, patterned bullets. 15+ games atm. So many fanworks, it's not even funny.
Seihou: Western Story. Virtually non-existent in terms of popularity. Made by the circle ZUN was once a part of. Mostly female cast with notable male characters. Characters mostly recycled from previous games. Focused on fewer, faster bullets. 3(+?) games atm. First 2 games featured characters from Touhou (since ZUN, the creator was involved in the creation of those 2 games). I posted the only fanwork I found.
Basically, Seihou, while interesting, isn't all that worth it to really get into. Want me should go on about Uwabami Breakers now?