horse wrangler vs puncher

horse wrangler and puncher both are nouns.

Word	Noun	Adjective	Verb	Adverb
horse wrangler	Yes	No	No	No
puncher	Yes	No	No	No

As nouns, puncher is a hypernym of horse wrangler; that is, puncher is a word with a broader meaning than horse wrangler:

horse wrangler: a cowboy who takes care of the saddle horses
puncher: a hired hand who tends cattle and performs other duties on horseback

Other hypernyms of horse wrangler include cowhand, cowherd, cowpoke, cowpuncher.

horse wrangler (noun)	puncher (noun)
a cowboy who takes care of the saddle horses	a tool for making holes or indentations
	a hired hand who tends cattle and performs other duties on horseback
	someone who delivers punches