busy vs work

busy is not a noun while work is a noun.

Word	Noun	Adjective	Verb	Adverb
busy	No	Yes	Yes	No
work	Yes	No	Yes	No

As verbs, work is a hypernym of busy; that is, work is a word with a broader meaning than busy:

busy: keep busy with
work: exert oneself by doing mental or physical work for a purpose or out of necessity; work

busy (noun)	work (noun)
	activity directed toward making or doing something
	the occupation for which you are paid
	a product produced or accomplished through the effort or activity or agency of a person or thing
	a place where work is done
	the total output of a writer or artist (or a substantial part of it)
	applying the mind to learning and understanding a subject (especially by reading)
	(physics) a manifestation of energy; the transfer of energy from one physical system to another expressed as the product of a force and the distance through which it moves a body in the direction of that force

busy (adjective)	work (adjective)
actively or fully engaged or occupied
overcrowded or cluttered with detail
intrusive in a meddling or offensive manner
(of facilities such as telephones or lavatories) unavailable for use by anyone else or indicating unavailability; (`engaged' is a British term for a busy telephone line)
crowded with or characterized by much activity

busy (verb)	work (verb)
keep busy with	give a workout to
	arrive at a certain condition through repeated motion
	go sour or spoil
	cause to undergo fermentation
	find the solution to (a problem or question) or understand the meaning of
	use or manipulate to one's advantage
	to mix into a homogeneous mass
	perform as expected when applied
	move into or onto
	shape, form, or improve a material
	cause to happen or to occur as a consequence
	prepare for crops
	make something, usually for a specific function
	gratify and charm, usually in order to influence
	proceed along a path
	move in an agitated manner
	provoke or excite
	be employed
	cause to work
	exert oneself by doing mental or physical work for a purpose or out of necessity; work
	have an effect or outcome; often the one desired or expected
	operate in a certain place, area, or specialty
	proceed towards a goal or along a path or through an activity
	have and exert influence or effect
	operate in or through
	cause to operate or function
	behave in a certain way when handled