budget vs work out

budget is a noun but work out is not a noun.

Word	Noun	Adjective	Verb	Adverb
budget	Yes	No	Yes	No
work out	No	No	Yes	No

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

Other hypernyms of budget include calculate, cipher, compute, cypher, figure, reckon.

budget (noun)	work out (noun)
a sum of money allocated for a particular purpose
a summary of intended expenditures along with proposals for how to meet them

budget (verb)	work out (verb)
make a budget	do physical exercise
	give a workout to
	come up with
	work out in detail
	find the solution to (a problem or question) or understand the meaning of
	make a mathematical calculation or computation
	be calculated
	happen in a certain way, leading to, producing, or resulting in a certain outcome, often well