tail lamp vs taillight

tail lamp and taillight both are nouns.

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

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

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

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

tail 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