six-shooter vs handgun

six-shooter and handgun both are nouns.

Word	Noun	Adjective	Verb	Adverb
six-shooter	Yes	No	No	No
handgun	Yes	No	No	No

As nouns, handgun is a hypernym of six-shooter; that is, handgun is a word with a broader meaning than six-shooter:

six-shooter: a pistol with a revolving cylinder (usually having six chambers for bullets)
handgun: a firearm that is held and fired with one hand

Other hypernyms of six-shooter include pistol, shooting iron, side arm.

six-shooter (noun)	handgun (noun)
a pistol with a revolving cylinder (usually having six chambers for bullets)	a firearm that is held and fired with one hand