What is the difference between 群 and 羣?
羣 is an archaic variant of 群. That is, although they mean the same thing, you would use 群 nowadays.

Interestingly, 羣 appears to have been the "correct" version in the past, and at some point 群 took that place:


There is a Three Kingdoms politician by the name of 陳羣, whereas the identically named Republican politician 陳群, use different characters in the last name.
The Kangxi dictionary entry for 群 states that it is a "vulgar variant" (《五經文字》羣，俗作群。), so the transition was at least between Qing and Republic of China.