A Fedora is a soft-brimmed hat with a unique indented crown, usually creased down the middle and pinched at the front. It has a flexible brim that often turns down. Fedoras are traditionally made from felt, but straw versions are also stylish for summer.
A Trilby hat also features a pinched, indented crown like a Fedora, but its brim is shorter, slopes down in the front, and turns up a bit at the back.
The Trilby is seen as a casual or smart-casual hat, great for daytime wear. The Fedora is considered more formal and works well for both semi-formal and formal occasions.