idea vs concept

idea and concept both are nouns.

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

As nouns, concept is a hyponym of idea; that is, concept is a word with a more specific, narrower meaning than idea:

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

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