set on fire vs set afire

set on fire and set afire both are verbs.

Word	Noun	Adjective	Verb	Adverb
set on fire	No	No	Yes	No
set afire	No	No	Yes	No

As verbs, set on fire and set afire are synonyms defined as:

Other synonyms of set on fire include set ablaze, set aflame.

set on fire (verb)	set afire (verb)
set fire to; cause to start burning	set fire to; cause to start burning