first gear vs gear mechanism

first gear and gear mechanism both are nouns.

Word	Noun	Adjective	Verb	Adverb
first gear	Yes	No	No	No
gear mechanism	Yes	No	No	No

As nouns, gear mechanism is a hypernym of first gear; that is, gear mechanism is a word with a broader meaning than first gear:

first gear: the lowest forward gear ratio in the gear box of a motor vehicle; used to start a car moving
gear mechanism: a mechanism for transmitting motion for some specific purpose (as the steering gear of a vehicle)

Other hypernyms of first gear include gear.

first gear (noun)	gear mechanism (noun)
the lowest forward gear ratio in the gear box of a motor vehicle; used to start a car moving	a mechanism for transmitting motion for some specific purpose (as the steering gear of a vehicle)