The difference is actually quite simple.

A hat is circular in shape with a brim or the visor going completely around it. Think of a cowboy Hat.

Yes, that's a hat.

Now, a Cap is a modern-day headwear with just a front brim and a fitted or snapback.

To understand the variations in detail, read the differences below

Cap

Caps make a more casual, modern statement
Has a visor - flat or curved or no visor at all - such as beanie
The fit is stronger on the head. Crown first your head
Blocks sunlight from your face. Beanies provide protection during winter as they cover your ears.
Used by athletes and fashion

Hat

Hats make a bold fashion statement
The brim circles the entire head - for example - https://capbargain.com/p?is_search=true&search_multi_match=fedora?ordering=popularity
The fit of the crown is loose on the head.
Since the brim is round, sunlight is blocked from the entire face.
Used for fashion and formal wear

Hope you are clear now.

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