fact vs concept

fact and concept both are nouns.

Word	Noun	Adjective	Verb	Adverb
fact	Yes	No	No	No
concept	Yes	No	No	No

As nouns, concept is a hypernym of fact; that is, concept is a word with a broader meaning than fact:

fact: a concept whose truth can be proved
concept: an abstract or general idea inferred or derived from specific instances

Other hypernyms of fact include conception, construct.

fact (noun)	concept (noun)
a piece of information about circumstances that exist or events that have occurred	an abstract or general idea inferred or derived from specific instances
a concept whose truth can be proved
a statement or assertion of verified information about something that is the case or has happened
an event known to have happened or something known to have existed