old geezer vs old man

old geezer and old man both are nouns.

Word	Noun	Adjective	Verb	Adverb
old geezer	Yes	No	No	No
old man	Yes	No	No	No

As nouns, old man is a hypernym of old geezer; that is, old man is a word with a broader meaning than old geezer:

Other hypernyms of old geezer include graybeard, greybeard, Methuselah.

old geezer (noun)	old man (noun)
an elderly man	an informal term for your father
	a man who is very old
	a familiar term of address for a man
	(slang) boss
	aromatic herb of temperate Eurasia and North Africa having a bitter taste used in making the liqueur absinthe