Good question! The only fool-proof way is to look at the teeth when the mouth is closed. If you see only top teeth, it's an alligator (their bottom teeth fit into grooves in the upper jaw and are hidden). If you see the bottom teeth pointing upwards (especially the 4th tooth) it's a croc. Crocs have a much more snaggled smile!

(The last picture would actually be a crocodile. Shhhh, don't tell anyone!)