illegitimate vs offspring

illegitimate and offspring both are nouns.

Word	Noun	Adjective	Verb	Adverb
illegitimate	Yes	Yes	No	No
offspring	Yes	No	No	No

As nouns, offspring is a hypernym of illegitimate; that is, offspring is a word with a broader meaning than illegitimate:

Other hypernyms of illegitimate include issue, progeny.

illegitimate (noun)	offspring (noun)
the illegitimate offspring of unmarried parents	any immature animal
	something that comes into existence as a result
	the immediate descendants of a person

illegitimate (adjective)	offspring (adjective)
of marriages and offspring; not recognized as lawful
contrary to or forbidden by law