The difference between a hat vs cap is one of semantics. A cap is a type of hat designed with specific features focused on comfort and essential style. The most significant difference between a hat vs cap is the type of crown and the option of a brim.
A hat is any round head covering with a shaped crown and a brim. Hats come in a variety of shapes and sizes and serve many purposes.
A cap is the second main style of headwear, which, like a hat, can be identified by the presence of two distinctive features. Caps are styled with a fitted, unshaped crown and most have a visor at the front instead of a full brim. Again, as with hats, there are several different types of caps, each with its own unique design.
Generally speaking, there isn’t a literal, physical difference between the two. A cap is considered a type (or category) of hat. So, the difference between a hat vs cap comes down to individual terminology. The word "hat" refers to any hat that covers your head, with many styles boasting a brim or visor. A "cap" is a hat that comes in a specific set of styles, with an unshaped crown and (usually) a visor in the front.