I have heard that it is not actually water that warms the wetsuit, but small bubbles inside the suit material? I can't seem to find any information besides" water gets in the suit and it warms up" which doesn't seem right to me, since I know my suit doesn't let in water.
If you have a WETsuit, it most certainly gets wet. There are dry suits out there too, maybe you surf in one of those? For the most part that's all a wet suit does, insulates your body and lets a little water in that your body will warm up.
Your body is the only source of heat, and the only keeping you warm. Your wetsuit is just an insulator between your body and cold water and air. trapped air is an excellent insulator, better than rubber, so todays really warm neoprene is pumped full of air or has a honeycomb structure. A paper thin layer of water trapped between your body and the wetsuit (where it gets in) provides a bit of additional insulation, but with the high insulating properties of todays neoprene, its probably not significant. 30 years ago when wetsuits felt like nearly solid rubber that layer of water might have been a little bit more of a factor, and believe me there was more of it!