child vs offspring

child and offspring both are nouns.

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

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

Other hypernyms of child include issue, progeny.

child (noun)	offspring (noun)
a young person of either sex	any immature animal
a human offspring (son or daughter) of any age	something that comes into existence as a result
an immature childish person	the immediate descendants of a person
a member of a clan or tribe