old man vs old geezer

old man and old geezer both are nouns.

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

As nouns, old geezer is a hyponym of old man; that is, old geezer is a word with a more specific, narrower meaning than old man:

Other hyponyms of old man include codger, old codger, antique, gaffer, old-timer, oldtimer, patriarch.

old man (noun)	old geezer (noun)
an informal term for your father	an elderly man
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