Boater hats are typically made of a very stiff straw, they have a relatively shallow oval crown with a flat top and straight sides, and a flat oval brim, and usually a grosgrain ribbon trim. Traditionally boaters have have been mens hats, but recently the ladies have claimed them for themselves swapping the traditional materials and playing around with brim and crown proportions, and making (we think!) altogether more interesting hats. Style your boater at an angle or sat to the back of your head.
Bretons, typically like boaters have oval crowns with usually flat tops and straight sides although occasionally wil have domed crowns, and they have have a turned up brim which opens out the face. They typically sit to the back of the head.
The Pork Pie hat, is a derivative of the boater style, with its shallow straight crowm but very shallow and almost non-existent brim. It gets its name from the shape of the top of the crown which is domed and ridged almost like the top of a pork pie. More stylish, but less tasty than an actual pork-pie though!