Hats and caps are the same thing depending on the version of English being used - British or American.
I came here to say the same thing :D Hats should also be an acceptable answer Imo
I (Midwestern American English) see a clear distinction between 'hat' and 'cap'. Hats tend to be formal and have a brim; caps tend to be casual or used in athletics, like a baseball cap. (But I understand that in the Pacific Northwest of the US they say 'baseball hat!')
Is 'sapkában a mistake here? should it not be 'sapkákban? 'I'm not realy sure on this one.
In these situations the singular is used. Similarly Nadrágban vagyunk and Ingben vagyunk and so on. The idea behind the singular is that everyone only has one cap. Using sapkák would tend to suggest that each person is wearing multiple caps.
I think that it was a trap : I suppose we need to use a plural (caps) and not a singular (hat).
Wouldn't the plural then be Sapkákban? Because Sapka, and Sapkában both use the hungarian singular for hat.