Normally I would not care which of "clubs" or "teams" is used, because I don't like WP:ENGVAR fist-shaking matches, but I think that we should use "teams" in this case simply because it is not ambiguous with any other kind of organization. The "clubs" name should have a soft redir. at it. This merge should not affect the child category names that prefer "clubs" in certain sports or in certain countries instead of "teams" (any similar club/team content forks that have happened by accident can be merged later, but mostly the categories are either "teams" or "clubs", not both, so it's not a large problem).
If the odd case arises that a particular club (in the broad sense of a team and the corporate entity that surrounds it) actually fields multiple teams (in the narrow sense of a specific set of individuals playing together at the same time in the same uniform), and the club and the teams are all independently notable, that's a case-by-case basis matter, and can be handled by the "Foo team A" and "Foo team B" and overarching "Foo club" article all being in "Category:Foo club". Or whatever. I.e., don't over-think it.
In the interim, I've cross-categorized Category:Sports clubs and Category:Sports teams so people can find the team/club they're looking for, if they're lucky and persistent. — SMcCandlish ☺ ☏ ¢ ≽ʌⱷ҅ᴥⱷʌ≼ 09:25, 27 February 2016 (UTC)
((cat see also))
is. --PanchoS (talk) 22:13, 29 May 2016 (UTC)