campsite vs camping site

campsite and camping site both are nouns.

Word	Noun	Adjective	Verb	Adverb
campsite	Yes	No	No	No
camping site	Yes	No	No	No

As nouns, campsite and camping site are synonyms defined as:

campsite and camping site: a site where people on holiday can pitch a tent

Other synonyms of campsite include bivouac, campground, camping area, camping ground, encampment.

campsite (noun)	camping site (noun)
a site where people on holiday can pitch a tent	a site where people on holiday can pitch a tent