school of thought vs belief

school of thought and belief both are nouns.

Word	Noun	Adjective	Verb	Adverb
school of thought	Yes	No	No	No
belief	Yes	No	No	No

As nouns, belief is a hypernym of school of thought; that is, belief is a word with a broader meaning than school of thought:

school of thought: a belief (or system of beliefs) accepted as authoritative by some group or school
belief: any cognitive content held as true

school of thought (noun)	belief (noun)
a belief (or system of beliefs) accepted as authoritative by some group or school	any cognitive content held as true
	a vague idea in which some confidence is placed