cowboy vs adult male

cowboy and adult male both are nouns.

Word	Noun	Adjective	Verb	Adverb
cowboy	Yes	No	No	No
adult male	Yes	No	No	No

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

cowboy: a male hired hand who tends cattle and performs other duties on horseback
adult male: an adult person who is male (as opposed to a woman)

Other hypernyms of cowboy include cowhand, cowherd, cowpoke, cowpuncher, puncher, man.

cowboy (noun)	adult male (noun)
someone who is reckless or irresponsible (especially in driving vehicles)	an adult person who is male (as opposed to a woman)
a performer who gives exhibitions of riding and roping and bulldogging
a male hired hand who tends cattle and performs other duties on horseback