Perhaps this is the wrong place for this, but what is the difference between a cap (czapka) and a hat (kapelusz)? In my native english dialect, they are synonyms.
Look at images on Google. Simply "kapelusz" has a brim around. For example cowboys wear them.
Your links do not work but that makes sense, partially. What about baseball caps/hats which have a brim, but not all the way around?
It's called "czapka" or "czapka z daszkiem".
When are you wearing a hat? - Why is this wrong?
Hey Jellei, 'when do you wear hat' and 'when do you wear a hat'. What difference does 'a' make while framing sentence in polish?
For Polish it doesn't make any difference, but your English sentence needs to be grammatically correct in English, and I don't believe that "When do you wear hat?" is...