How far back do you wish to go? Long long ago hats were a sign of a female's status. Married women and those with children wore hats as a sign of respectability. Unmarried women were hatless.
A cap has no brim, however it may have a visor.
A hat may or may not have a brim but is generally fancier, or more formal.
The term "feather in your cap" stems from the Native American habit of plucking a feather fro a bird and then releasing the bird saving the feather for his headdress, each feather being a sign of bravery.
Speaking of Native Americans, Why did the chief call his son 98 cents?
Because he wasn't a buck yet.....
Sorry, I just thought it would be good to "cap" off this post. :smile2: