believe vs think

believe is not a noun while think is a noun.

Word	Noun	Adjective	Verb	Adverb
believe	No	No	Yes	No
think	Yes	No	Yes	No

As verbs, believe and think are synonyms defined as:

Other synonyms of believe include conceive, consider.

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

believe (noun)	think (noun)
	an instance of deliberate thinking

believe (verb)	think (verb)
accept as true; take to be true	bring into a given condition by mental preoccupation
follow a credo; have a faith; be a believer	use or exercise the mind or one's power of reason in order to make inferences, decisions, or arrive at a solution or judgments
credit with veracity	judge or regard; look upon; judge
be confident about something	recall knowledge from memory; have a recollection
judge or regard; look upon; judge	expect, believe, or suppose
	have in mind as a purpose
	be capable of conscious thought
	focus one's attention on a certain state
	decide by pondering, reasoning, or reflecting
	ponder; reflect on, or reason about
	have or formulate in the mind
	dispose the mind in a certain way
	imagine or visualize