Good question Maria,
Waterspouts are just tornadoes that are over water. They can form from the same dynamics as a land tornado, from a rotating thunderstorm (supercell).
There are also fair weather waterspouts which are the more common variety, and much weaker. It`s my belief they can form from a land and sea breeze convergence causing rotation, sometimes a towering cumulus can provide enough updraft. Another idea, later in the summer when sea temps reach their peak, a cold dry airmass can move over those high water temps to create an unstable and convective airmass, enough to provide rotation and updraft.
The difference between the two, the tornadic variety will drop from the storm itself, where as a fair weather variety begins from the surface and rises.
That`s my take!!