I know of two types of bits called Tom Thumb, a fixed cheek like this, or one with a loose ring like a fulmer. Pretty common in driving, racing and on ponies.
The way I see it, TT bits are short-cheek versions of the full cheek/fulmer. Definitely not a leverage bit. So what else is a Tom Thumb? I'd like to know because if it's as nasty as people say, I want to avoid it.