number vs count

number and count both are nouns.

Word	Noun	Adjective	Verb	Adverb
number	Yes	No	Yes	No
count	Yes	No	Yes	No

As nouns, count is a hyponym of number; that is, count is a word with a more specific, narrower meaning than number:

As verbs, number and count are synonyms defined as:

Other synonyms of number include enumerate, numerate.

As verbs, number and count are synonyms defined as:

number (noun)	count (noun)
an item of clothing	the act of counting; reciting numbers in ascending order
the property possessed by a sum or total or indefinite quantity of units or individuals	a nobleman (in various countries) having rank equal to a British earl
a clothing measurement	the total number counted
one of a series published periodically
a symbol used to represent a number
a numeral or string of numerals that is used for identification and may be attached to accounts, memberships, etc.
the number is used in calling a particular telephone
a short performance that is part of a longer program
the grammatical category for the forms of nouns and pronouns and verbs that are used depending on the number of entities involved (singular or dual or plural)
a numbered item in a series
a select company of people
a concept of quantity involving zero and units

number (verb)	count (verb)
place a limit on the number of	include as if by counting
determine the number or amount of	have faith or confidence in
enumerate	take account of
give numbers to	determine the number or amount of
add up in number or quantity	name or recite the numbers in ascending order
put into a group	show consideration for; take into account
	have weight; have import, carry weight
	put into a group
	have a certain value or carry a certain weight