Paging the Arcmeister....
Arc is not only one of the top ski instructors in the world--and one of our own EpicSki Academy coaches--but he is an outstanding water skier as well. He'll certainly have some valid input here, if he's around. If he says anything that contradicts what I'm about to say, he's probably right. Arc?
Personally, I've water skied a LITTLE, and not at all for at least 5 years. But I've always found water skiing easy, at least at the "hack" level that I've played with it, and I'm sure it is because of the similarities to snow skiing.
I would suggest, though, that the similarities are less in the specific, individual movements, and more in the overall sense of gliding and balancing while linking turns at high speed, and the underlying abilities and experience that develop these skills. The two sports probably generate more g-forces than anything else we do while balancing on our feet. There is a lot of useful "transfer" from that fact alone.
But water skiing is not snow skiing. Some of the movements are similar, but not the same, as many water skiers have discovered their first time on real (pardon my bias!) skis. One well-known tendency of water skiers is to lean back on snow skis and fall over. Water skiers may well balance farther back on their equipment than snow skiers, but at least part of the difference in positions results from the water skier's need to balance against the rope pulling on their arms and shoulders.
One of the classic differences between snow and water skiing has actually diminished somewhat in recent years. Getting high performance from snow skis used to require very high edge angles, which necessitated often extreme hip and knee angulation. Today's skis carve clean with less edge angle, and easily generate high g-forces that require the skier to lean strongly into the turn ("incline") for balance. Today's skiing generally involves more inclination and less angulation than in the past--much like water skiing.
Again, if you look at the individual little movements, you will see distinct differences. If you look at the bigger picture of balancing while linking direction changes at high speed, and using your body to tip, manage pressure fore and aft, and control the direction of the tool attached to your feet--that statement describes both sports equally well.
One thing that does differentiate snow skiing from water skiing is that water is pretty much always water, and it's always level, if not necessarily flat and smooth. But snow conditions vary with every turn, as does the pitch and contour of the terrain. Even though water may well have waves, water skiers (at least those I know) rarely seek them out for fun. But varied conditions and terrain are the essence of great skiing, part of the challenge and joy of a day in the mountains.
Because on snow, no two turns ever take place under truly identical conditons, snow skiing involves an added challenge over water skiing. Knowledgeable water skiers may argue otherwise, but I submit that water skiing relies mostly on "habitual skills"--the practiced ability to do the same thing the same way over and over. Snow skiing also involves habitual skills, but adds the need for refined "perceptual skills"--the skill of reading the terrain, picking good lines, and reacting to unexpected forces, with a larger quiver of technical and tactical options. This aspect, to me, is the greatest difference between the two sports. Well, that, and bikinis, of course.