acrobatics vs gymnastics

acrobatics and gymnastics both are nouns.

Word	Noun	Adjective	Verb	Adverb
acrobatics	Yes	No	No	No
gymnastics	Yes	No	No	No

As nouns, gymnastics is a hypernym of acrobatics; that is, gymnastics is a word with a broader meaning than acrobatics:

acrobatics: the gymnastic moves of an acrobat
gymnastics: a sport that involves exercises intended to display strength and balance and agility

Other hypernyms of acrobatics include gymnastic exercise.

acrobatics (noun)	gymnastics (noun)
the gymnastic moves of an acrobat	a sport that involves exercises intended to display strength and balance and agility
the performance of stunts while in flight in an aircraft