gymnastic exercise vs gymnastics

gymnastic exercise and gymnastics both are nouns.

Word	Noun	Adjective	Verb	Adverb
gymnastic exercise	Yes	No	No	No
gymnastics	Yes	No	No	No

As nouns, gymnastic exercise and gymnastics are synonyms defined as:

gymnastic exercise and gymnastics: a sport that involves exercises intended to display strength and balance and agility

gymnastic exercise (noun)	gymnastics (noun)
(gymnastics) an exercise designed to develop and display strength and agility and balance (usually performed with or on some gymnastic apparatus)	a sport that involves exercises intended to display strength and balance and agility
a sport that involves exercises intended to display strength and balance and agility