meter vs common measure

meter and common measure both are nouns.

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

As nouns, common measure is a hyponym of meter; that is, common measure is a word with a more specific, narrower meaning than meter:

Other hyponyms of meter include catalexis, scansion, common meter, foot, metrical foot, metrical unit.

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

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