I'm pretty sure the thin one goes on the drain plug. I fit it on there, and screwed it into the float bowl and it went in good. Where as, when I put the fat one on it, screwed it in, it didn't screw in all the way...I still don't really know!
Edit: As a matter of fact, I think the thin one does go on the float seat instead. It just fit on easier. But still, if there's someone who can help me confirm this I'd appreciate it!