Usually you have to move at least a certain number of air miles from your current camp after you exceed the stay limit to continue camping on public land. The distance varies by jurisdiction, on BLM land in Arizona it's 25 miles, Colorado national forests require 30 miles seperation. There's also a time limit before you can return to an area, usually 14 days.
The idea is to prevent people from semi-permantly residing in an area by just moving a short distance and then returning.
Whether you move from one forest to another is irrelevant.