The one Carnival uses is actually referred to as the Carnival Pier (dont know if thats what its really called). It's about a 6 minute taxi ride into the center of San Miguel. There are two others closer to town. One of which is basically right in town.
I believe Carnival built this pier, and there are quite a few small shop, bars and restauarnts right there.
If you go to the web site "Cozumel Insider" and scroll down toward the bottom, you will find the listing for all of the ships coming in to port. There are three docks in Cozume. Most of the Cranival ships dock at Punta Maya, which is a new downtown dock. It is in the center on San Miguel. We have walked the distance to the end of all the recommended shops and was not worth the six dollar taxi ride. The other large pier is the International pier and sometimes a Carnival ship will dock there too. Hope this helps.
The Puerta Maya dock was built by Carnival and Carnival has first priority on using it, however if the Puerta Maya dock is full you may dock else where. It is right next to the international pier which is used primarily by RCCL.