A campsite could be anything from simply where a unit stopped marching for the night, or part of a night, to a place where a unit stayed for a few days, to where a unit spent the winter.
A field headquarters suggests a larger unit or group of units, and tents, etc- probably a more formalized campsite.
In terms of geographical area, it's hard to say. A field headquarters would take up more area than a small unit's campsite, but much less than a large unit's campsite. I suspect in most cases, a field headquarters would take up a smaller area than a campsite.