headlamp vs headlight

headlamp and headlight both are nouns.

Word	Noun	Adjective	Verb	Adverb
headlamp	Yes	No	No	No
headlight	Yes	No	No	No

As nouns, headlamp and headlight are synonyms defined as:

headlamp and headlight: a powerful light with reflector; attached to the front of an automobile or locomotive

headlamp (noun)	headlight (noun)
a powerful light with reflector; attached to the front of an automobile or locomotive	a powerful light with reflector; attached to the front of an automobile or locomotive