assess vs score

assess is not a noun while score is a noun.

Word	Noun	Adjective	Verb	Adverb
assess	No	No	Yes	No
score	Yes	No	Yes	No

As verbs, score is a hyponym of assess; that is, score is a word with a more specific, narrower meaning than assess:

assess: evaluate or estimate the nature, quality, ability, extent, or significance of
score: assign a grade or rank to, according to one's evaluation

Other hyponyms of assess include grade, mark, rate, value, standardise, standardize, reassess, reevaluate, censor, praise.

assess (noun)	score (noun)
	the act of scoring in a game or sport
	a seduction culminating in sexual intercourse
	a number or letter indicating quality (especially of a student's performance)
	the facts about an actual situation
	a written form of a musical composition; parts for different instruments appear on separate staves on large pages
	a resentment strong enough to justify retaliation
	a set of twenty members
	grounds
	a number that expresses the accomplishment of a team or an individual in a game or contest
	a slight surface cut (especially a notch that is made to keep a tally)
	an amount due (as at a restaurant or bar)

assess (verb)	score (verb)
evaluate or estimate the nature, quality, ability, extent, or significance of	assign a grade or rank to, according to one's evaluation
estimate the value of (property) for taxation	make underscoring marks
set or determine the amount of (a payment such as a fine)	gain points in a game
charge (a person or a property) with a payment, such as a tax or a fine	get a certain number or letter indicating quality or performance
	make small marks into the surface of
	induce to have sex
	write a musical score for