I'm looking at this script for possibly using for a gallery site, but I can't seem to figure out how or if you can add categories to your gallery.

Do you mean categories for the photos? Basically you can create as many galleries as needed each with their own title/topic.

So could I make a car topic with Ford and Chevy underneath that for instance?

When you create a new forum, just select the parent forum...

Category
-Parent Forum
--Child Forum

So:
Gallery Forums
-Cars
--Ford
--Chevy

Are there any settings I would need to set to distinguish image gallery categories and just a regular forum post?

The primary one when creating the forum, you just need to choose the "Is Gallery" option upon creation. At that point the forum will contain photos instead of posts as the primary content.