common land vs pasture land

common land and pasture land both are nouns.

Word	Noun	Adjective	Verb	Adverb
common land	Yes	No	No	No
pasture land	Yes	No	No	No

As nouns, pasture land is a hypernym of common land; that is, pasture land is a word with a broader meaning than common land:

common land: a pasture subject to common use
pasture land: a field covered with grass or herbage and suitable for grazing by livestock

Other hypernyms of common land include grazing land, lea, ley, pasture, pastureland.

common land (noun)	pasture land (noun)
a pasture subject to common use	a field covered with grass or herbage and suitable for grazing by livestock