Difference between water and tea
Your question is very awkward.

Let's define Tea as boiling leaves in water. At the end, you remove the leaves and drink the flavoured water.

At this point, the "tea" is still very much water - as in tea is water with dissolved chemicals from the leaves. Note, the word chemicals is not to be interpreted in a negative way because everything (including water) is a chemical.

So, the difference between tea and water are the chemicals that dissolve. What are these chemicals? The answer to that depends very much on the tea. Another difference is the temperature - tea is typically hot.

You can look at this article about chemicals in green tea and their associated health benefits. You can do further searches for other tea types and for each of those chemicals.

In short, no you do not get dehydrated because of tea vs. water. Dry skin can be caused by a lot of different reasons. Oh and no, caffeine doesn't cause any significant amount of dehydration as far as I know.