old man vs old-timer

old man and old-timer both are nouns.

Word	Noun	Adjective	Verb	Adverb
old man	Yes	No	No	No
old-timer	Yes	No	No	No

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

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

old man (noun)	old-timer (noun)
an informal term for your father	an elderly man
a man who is very old	an experienced person who has been through many battles; someone who has given long service
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