I've noticed that some posted photos appear as full-size photos while other show up at thumbnail attachments. Can anyone tell me what determines how a photo will appear? Are larger photo files automatically turned into thumbnails?

A full-size picture is stored on a web server somewhere, and there's a link to it within the post. Quote a post and see.

A thumbnail represents a picture uploaded from the posters harddrive as an attachement to the post. The "Manage attachments"-button is located below the post edit window, you can attach two pictures per post.