Yes, U is left to right (similar to X on a standard 2D XY plane) and V is up and down.
U and V are also industry standard terminology for many other direction definitions, not just 2D cad work. That's why it omits the X and Y portions. For example, when talking about a complex (swoopy) surface, there is a U and V direction of the surface, which changes X and Y directions because of the countour of the surface. It can get pretty tricky, and very confusing if X and Y were included.
Not to mention, U is sometimes the substitute for micro. Doesn't make sense in this context, but could be confusing. U is also used to imply a relative change, similar to dX or dy. In this case, that context is spot-on, but may not always be. I hope you don't mind the long story.