idea vs cogitation

idea and cogitation both are nouns.

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

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

idea (noun)	cogitation (noun)
the content of cognition; the main thing you are thinking about	attentive consideration and meditation
your intention; what you intend to do	a carefully considered thought about something
an approximate calculation of quantity or degree or worth
a personal view
(music) melodic subject of a musical composition