count vs number

count and number both are nouns.

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

As nouns, number is a hypernym of count; that is, number is a word with a broader meaning than count:

As verbs, count and number are synonyms defined as:

Other synonyms of count include enumerate, numerate.

As verbs, count and number are synonyms defined as:

count (noun)	number (noun)
the act of counting; reciting numbers in ascending order	an item of clothing
a nobleman (in various countries) having rank equal to a British earl	the property possessed by a sum or total or indefinite quantity of units or individuals
the total number counted	a clothing measurement
	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

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