Some teams have traditional "theories" of play, but that also does have a lot to do with certain managers. Ex. Arsene Wegner at Arsenal play "slick, passing football" - this identity is likely wrapped up in the fact that Wegner has been there for so long, though.
Mourinho plays defensive, counterattacking football wherever he goes. Inter, Madrid, and Chelsea all did/do this under him.
Guardiola at Barça and Bayern is the prime example of "possession football."