plan vs lay out

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

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

As verbs, lay out is a hyponym of plan; that is, lay out is a word with a more specific, narrower meaning than plan:

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

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