What I always wanted to know:
If you put a thing on your head, when is it called a cap and when is it a hat? I remember having read about "woolen hats" as in knitted. A thing like that in Germany would be a cap (Kappe or Mütze).
However a stiff thing like what today's adorable COTD is wearing would be a hat (Hut).
A baseball hat would always be a cap and never a hat.
I feel that things are sorted differently in English. Looking forward to an intense discussion about top-of-head ornaments