How many kinds of auto racing are there?

Just wondering. Last night on TV I saw a clip from a race involving cars with a tiny cab at back and a long, narrow body – something clearly designed specifically for racing, probably not even street-legal – and I had no idea what that vehicle, or style of racing, is called.

Anything with wheels can (and will) be raced in some fashion.

Your description sounds like a Top Fuel dragster, which is basically an aluminum ladder with a grenade strapped to the back.

Did it look like this?

Yes.