six-shooter vs six-gun

six-shooter and six-gun both are nouns.

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

As nouns, six-shooter and six-gun are synonyms defined as:

six-shooter and six-gun: a pistol with a revolving cylinder (usually having six chambers for bullets)

Other synonyms of six-shooter include revolver.

six-shooter (noun)	six-gun (noun)
a pistol with a revolving cylinder (usually having six chambers for bullets)	a pistol with a revolving cylinder (usually having six chambers for bullets)