concept vs idea

concept and idea both are nouns.

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

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

concept: an abstract or general idea inferred or derived from specific instances
idea: the content of cognition; the main thing you are thinking about

Other hypernyms of concept include thought.

concept (noun)	idea (noun)
an abstract or general idea inferred or derived from specific instances	the content of cognition; the main thing you are thinking about
	your intention; what you intend to do
	an approximate calculation of quantity or degree or worth
	a personal view
	(music) melodic subject of a musical composition