first lady vs married woman

first lady and married woman both are nouns.

Word	Noun	Adjective	Verb	Adverb
first lady	Yes	No	No	No
married woman	Yes	No	No	No

As nouns, married woman is a hypernym of first lady; that is, married woman is a word with a broader meaning than first lady:

Other hypernyms of first lady include wife.

first lady (noun)	married woman (noun)
the wife of a chief executive	a married woman; a man's partner in marriage
the leading woman in an art or profession