common measure vs meter

common measure and meter both are nouns.

Word	Noun	Adjective	Verb	Adverb
common measure	Yes	No	No	No
meter	Yes	No	Yes	No

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

Other hypernyms of common measure include beat, cadence, measure, metre.

common measure (noun)	meter (noun)
the usual (iambic) meter of a ballad	any of various measuring instruments for measuring a quantity
an integer that divides two (or more) other integers evenly	rhythm as given by division into parts of equal duration
a time signature indicating four beats to the bar	(prosody) the accent in a metrical foot of verse
	the basic unit of length adopted under the Systeme International d'Unites (approximately 1.094 yards)

common measure (verb)	meter (verb)
	measure with a meter
	stamp with a meter indicating the postage