common land vs pastureland

common land and pastureland both are nouns.

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

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

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

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

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