BoulderJohn's description is accurate. One other thing about the faster drift dives is that you may not be able to stop and enjoy everything. Sometimes, the current is just too strong to do so. I like to poke around and take a lot of time in relatively small areas, so some of the dives I have experienced in Cozumel have a bit frustrating from that point of view.
If you look carefully, you can usually find some dead coral and hook it with a single finger, and that should be enough to stop you. (That is the "problem" with Barracuda Reef--it is so healthy it is hard to find someplace to hold on.) You can also streamline your body so that you don't look so much like a sail. In some places you can duck into recesses in the coral.