Just to clarify a little . . . a cenote is, in fact, an opening into an underground water system. Many of them are sinkholes, where the roof has caved in and the rubble that fell makes an "island" or sometimes just piles of rock in the pool. Sometimes, the roof of the cave is above the waterline, and you can snorkel back under the rock. Some cenotes allow you to do this for quite some distance, like NoHoch and Yax Muul. Others have no air space under the roof, but open into broad rooms where there is space to swim around quite a bit before losing sight of sunlight. Among these are the ones that are typically used for tours for OW divers, such places as Chac Mool, Grand Cenote, Dos Ojos, Ponderosa, and Taj Maha.
Other cenotes have openings into tunnels, where there is little space that would be considered cavern, as you lose sight of light very quickly. These cenotes are only done by certified cave divers.
You can pay an entry fee and swim in many cenotes. But if a company is advertising tours for DIVERS, they are going into the overhead environment, and anyone booking such tours should know that.
