WW, i would use the word tam for a hat, made of cloth. The top of the hat would be a circle, and it would have sides of bias cut cloth, about 1 to 2 inches.. the sides would be finished in a leather binding, and have draw string to adjust the fit. A Tam may or may not be trimmed with a tassle or pom pom on the center top. A Tam o' Shanter, specifically, would be a Tam made from plaid or tartan cloth.

a beret, while similar in shape, and appearence, would be a one piece hat, formed of felt, with a self bound edge, and usually is a solid color.