For those of you new to hats, here’s a brief intro to terms and styles. For the sake of simplicity and easy reading, a lot of the finer points have been omitted, but this will at least get you started.
General Hat Styles

Common hat creases

Hat Parts

Types of Brim Edges

Types of sweatbands

Am not quite appreciating the difference here though I’m sure I’ll think how obvious once enlightened! Thanks, JFM
Pardon me, comment above is referring to the reeded vs unreeded.