Depending on your location and the local verbage, but a water bar and cross ditch are usually synonymous. On steeper roads, they are designed to do two things, get the water off the road surface and get the water out of the ditch and over bank on the downhill side.
Water flowing down the road and ditch has energy which can cause erosion. The steeper the road, the greater the energy. One of the keys to erosion control on roads is to get the water off the road and out of the ditch.
I'm talking about gravel roads in a forest environment.