testimony vs asseveration

testimony and asseveration both are nouns.

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

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

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

Other hypernyms of testimony include assertion, averment.

testimony (noun)	asseveration (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
something that serves as evidence