Cap usually refers to forms of headwear fitting very close to the head and without brim.
In Middle-earth many cultures preferred slightly conical or pointed caps resembling Phrygian caps or knit caps. Both Elves and some Northmen (those of Esgaroth) were depicted wearing these kinds of caps. The Hobbits also wore almost shapeless felt hats, maybe resembling medieval type hats with a pointed brim. Dwarves preferred pointed hoods or cowls similar to jelly bag caps. Elvish caps were also called "Togli".