I have to agree the Keys are a much better choice than Cozumel for beginners. Cozumel dives are almost exclusively live boating. I am very much against the practice because it simply isn't safe.
There are three methods of diving in current from an unanchored boat where you drift with the current. All three are commonly called "drift diving" although it is usually a misnomer.
Drift diving is rarely used. A weighted line, often the anchor line, is dropped to the desired dive depth. Divers descend along the line to the desired depth, holding on the line as the boat drifts along, they are always connected to the boat.
Live boating is common in Mexico, especially Cozumel. It is a fairly risky method. Divers descend and drift with the current. The boat follows the bubbles. Using this method, it is easy to lose divers or to accidentally strike a diver with the boat.
The preferred method is float diving. It is similar to live boating, except one of the divers has a reel attached to a float, which the boat follows. Divers stay close to the diver with the reel and therefore do not get lost. Divers ascend next to the line and stay next to the float until acknowledged by the boat crew. They then swim away from the float for pickup. This ensures the boat does not strike divers.
When I go to Cozumel, I take my own float and reel as I refuse to live boat.
Food for thought.
Walter