common measure vs four-four time

common measure and four-four time both are nouns.

Word	Noun	Adjective	Verb	Adverb
common measure	Yes	No	No	No
four-four time	Yes	No	No	No

As nouns, common measure and four-four time are synonyms defined as:

common measure and four-four time: a time signature indicating four beats to the bar

Other synonyms of common measure include common time, quadruple time.

common measure (noun)	four-four time (noun)
the usual (iambic) meter of a ballad	a time signature indicating four beats to the bar
an integer that divides two (or more) other integers evenly
a time signature indicating four beats to the bar