oil furnace vs oil burner

oil furnace and oil burner both are nouns.

Word	Noun	Adjective	Verb	Adverb
oil furnace	Yes	No	No	No
oil burner	Yes	No	No	No

As nouns, oil furnace and oil burner are synonyms defined as:

oil furnace (noun)	oil burner (noun)
a furnace that burns oil	a furnace that burns oil