I tend to think of the FFRF as sort of an atheist ACLU, and American Atheists as a more general purpose activism / advocacy group that focuses more on public policy rather than policing illegal theist overreach per se.

I go to a ton of metal/punk gigs here in LA. Those communities don't do much religion.

Similar in view, but I think FFRF is much more active on the legal front, keeping church out of government and schools. I am a proud member of FFRF, and I think Andrew Seidel should be on the Supreme Court.

I am not familiar with American Atheist. FFRF is an organization that often pursues legal resolution of issues affecting non-believers. If I’m not mistaken, they also facilitate publishing atheist authors and facilitate lectures. A quick search suggests that Americans atheist has similar goals and principles.