matron vs adult female

matron and adult female both are nouns.

Word	Noun	Adjective	Verb	Adverb
matron	Yes	No	No	No
adult female	Yes	No	No	No

As nouns, adult female is a hypernym of matron; that is, adult female is a word with a broader meaning than matron:

Other hypernyms of matron include nurse, woman.

matron (noun)	adult female (noun)
a married woman (usually middle-aged with children) who is staid and dignified	an adult female person (as opposed to a man)
a woman in charge of nursing in a medical institution
a wardress in a prison