lay out vs plan

lay out is not a noun while plan is a noun.

Word	Noun	Adjective	Verb	Adverb
lay out	No	No	Yes	No
plan	Yes	No	Yes	No

As verbs, plan is a hypernym of lay out; that is, plan is a word with a broader meaning than lay out:

lay out (noun)	plan (noun)
	scale drawing of a structure
	a series of steps to be carried out or goals to be accomplished
	an arrangement scheme

lay out (verb)	plan (verb)
get ready for a particular purpose or event	make plans for something
provide a detailed plan or design	have the will and intention to carry out some action
bring forward and present to the mind	make or work out a plan for; devise
lay out orderly or logically in a line or as if in a line
spend or invest