gearshift vs shifter

gearshift and shifter both are nouns.

Word	Noun	Adjective	Verb	Adverb
gearshift	Yes	No	No	No
shifter	Yes	No	No	No

As nouns, gearshift and shifter are synonyms defined as:

gearshift and shifter: a mechanical device for engaging and disengaging gears

Other synonyms of gearshift include gear lever, gearstick.

gearshift (noun)	shifter (noun)
a mechanical device for engaging and disengaging gears	a mechanical device for engaging and disengaging gears
	a stagehand responsible for moving scenery