testimony vs assertion

testimony and assertion both are nouns.

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

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

testimony: an assertion offering firsthand authentication of a fact
assertion: a declaration that is made emphatically (as if no supporting evidence were necessary)

Other hypernyms of testimony include asseveration, averment.

testimony (noun)	assertion (noun)
a solemn statement made under oath	a declaration that is made emphatically (as if no supporting evidence were necessary)
an assertion offering firsthand authentication of a fact	the act of affirming or asserting or stating something
something that serves as evidence