We actually have a lot of species of skate here. 8 that I know of.
The most common skate in our waters is the thorny skate, however, they are normally found in 50+ meters (and as deep as 1500m!) so scuba divers will not typically see them.
The second most common skate (according to trawl surveys by NMFS) is the little skate. This is also the most common skate in inshore waters where divers are likely to see them. Most of the skates you see are probably this one.
The third most common skate is the winter skate. You will see many of these but may not know it. This one is VERY tricky because it looks almost exactly like the little skate. A lot of people don't even realize they are different species. If you look at the key Matt provided a link to you may notice all of the characteristics given to tell these two species apart only work for specimens >35cm in length. Even then, they require you to look pretty closely. For the smaller ones, even the experts have a hard time telling them apart. It requires a very close up hands on examinination of the skate so you could not really tell when diving.
The smooth skate is common but it prefers deeper waters (30m or more) so you won't see too many of these diving.
We also have the barndoor skate but you probably won't see many of these either.
The other species are all very rare in our waters. These are the rosette skate, the deepwater skate, and the clearnose skate.