[gulpahum]

Do those moons really have a flowing ocean under the icy surface or is it water trapped in rocks?

Earth has a huge "ocean" deep in its mantle, but it's inside rocks. http://www.livescience.com/1312-huge-ocean-discovered-earth....

[kchangnyt]

Yes, these are flowing oceans. On Ganymede, it's an ocean between two layers of ice. On Enceladus, it's water below an icy crust and on top of a rocky core.