Difference between "encampment" and "camp"
Solution 1:
As literal nouns these words are synonymous, though "camp" is by far the more common term to describe a location for and collection of temporary accommodations and related activities. In modern usage, "encampment" is usually reserved for military contexts (and even there is rare and used for spice).
As a verb, the words differ: "to camp" is to engage in the activity of camping, i.e. "to go and live in a camp or as campers"; "to encamp" is specifically to "set up a camp".
But perhaps the biggest difference is that "camp" is used synecdochically to mean "the people of a camp", and by extension, metaphorically to mean "the members of a particular [often political] party". "Encampment" is never used this way (it always means the camp as a whole; the location, the structures, the people, the activity; but never only "the people").
Bottom line: contemporary English speakers almost always use "camp" today; the only time we'd use "encamp" is as a verb, to specifically describe the activity of "setting up a camp". The only time we'd really use "encampment" is as a colorful synonym for camp, almost always in a military context.
Solution 2:
Camp is basically short for encampment. Families camp out, but an army encamps itself at a location. This location is then called the encampment.