gearshift vs gear lever

gearshift and gear lever both are nouns.

Word	Noun	Adjective	Verb	Adverb
gearshift	Yes	No	No	No
gear lever	Yes	No	No	No

As nouns, gearshift and gear lever are synonyms defined as:

gearshift and gear lever: a mechanical device for engaging and disengaging gears

Other synonyms of gearshift include gearstick, shifter.

gearshift (noun)	gear lever (noun)
a mechanical device for engaging and disengaging gears	a mechanical device for engaging and disengaging gears