idea vs plan

idea and plan both are nouns.

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

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

idea (noun)	plan (noun)
the content of cognition; the main thing you are thinking about	scale drawing of a structure
your intention; what you intend to do	a series of steps to be carried out or goals to be accomplished
an approximate calculation of quantity or degree or worth	an arrangement scheme
a personal view
(music) melodic subject of a musical composition

idea (verb)	plan (verb)
	make plans for something
	have the will and intention to carry out some action
	make or work out a plan for; devise