The three most popular hat types for gentlemen in the Georgian era were the cocked hat, bicorne, and beaver hat.

Throughout the 18th century, gentlemen preferred the cocked hat. The bicorne became popular during the 1790s, and then the beaver hat dominated the fashion scene during the 19th century, especially during the Regency era.

As we reach the turn of the century, we have both the cocked hat (or the tricorne as we call it now) and the bicorne competing for attention. Typically, the cocked hat was most worn for informal, day wear, whereas the bicorne was most popular for formal, evening wear (and the chosen hat by the military). Important to note is the tricorne was not called the tricorne until the Victorian era. It would have been known as the cocked hat, predominately.

The beaver hat, which eventually became known as the top hat and stovepipe hat, came in a variety of different styles from round to narrow brims, brims up to brims down, etc. It was called the beaver hat because it used beaver felt on the outside, silk on the inside, and often suede around the brim to protect from sweat.

A must-read post on top hats:

https://regencygentleman.wordpress.com/tag/beaver-hat/

A lovely post on cocked hats:

https://twonerdyhistorygirls.blogspot.com/2010/10/now-for-gentleman-cocked-hat-c-1777.html