rear lamp vs taillight

rear lamp and taillight both are nouns.

Word	Noun	Adjective	Verb	Adverb
rear lamp	Yes	No	No	No
taillight	Yes	No	No	No

As nouns, rear lamp and taillight are synonyms defined as:

rear lamp and taillight: lamp (usually red) mounted at the rear of a motor vehicle

Other synonyms of rear lamp include rear light, tail lamp.

rear lamp (noun)	taillight (noun)
lamp (usually red) mounted at the rear of a motor vehicle	lamp (usually red) mounted at the rear of a motor vehicle