claim vs assertion

claim and assertion both are nouns.

Word	Noun	Adjective	Verb	Adverb
claim	Yes	No	Yes	No
assertion	Yes	No	No	No

As nouns, assertion is a hypernym of claim; that is, assertion is a word with a broader meaning than claim:

claim: an assertion of a right (as to money or property)
assertion: a declaration that is made emphatically (as if no supporting evidence were necessary)

Other hypernyms of claim include asseveration, averment.

As nouns, assertion is a hypernym of claim; that is, assertion is a word with a broader meaning than claim:

claim: an assertion that something is true or factual
assertion: a declaration that is made emphatically (as if no supporting evidence were necessary)

Other hypernyms of claim include asseveration, averment.

claim (noun)	assertion (noun)
demand for something as rightful or due	a declaration that is made emphatically (as if no supporting evidence were necessary)
an established or recognized right	the act of affirming or asserting or stating something
an informal right to something
an assertion of a right (as to money or property)
a demand
an assertion that something is true or factual

claim (verb)	assertion (verb)
assert or affirm strongly; state to be true or existing
take as an undesirable consequence of some event or state of affairs
ask for legally or make a legal claim to, as of debts, for example
lay claim to; as of an idea
demand as being one's due or property; assert one's right or title to