The Buffalo Club seems to be a social club/fraternal organization founded in 1867....

http://www.thebuffaloclub.org/

While the Buffalo Athletic Club was built in 1924, though probably established in 1889?

http://www.restaurantwarecollectors....+Athletic+Club

The Buffalo Bisons Base ball Club may have had some affiliation with both of these organizations (members of both, or all). Tough to say, everything is named after "Buffaloes" in Buffalo... even their chicken wings.