kindergartner vs child

kindergartner and child both are nouns.

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

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

Other hypernyms of kindergartner include fry, kid, minor, nestling, nipper, shaver, small fry, tiddler, tike, tyke, youngster.

kindergartner (noun)	child (noun)
a child who attends a preschool or kindergarten	a young person of either sex
	a human offspring (son or daughter) of any age
	an immature childish person
	a member of a clan or tribe