pommel horse vs gymnastic horse

pommel horse and gymnastic horse both are nouns.

Word	Noun	Adjective	Verb	Adverb
pommel horse	Yes	No	No	No
gymnastic horse	Yes	No	No	No

As nouns, gymnastic horse is a hypernym of pommel horse; that is, gymnastic horse is a word with a broader meaning than pommel horse:

pommel horse: a gymnastic horse with a cylindrical body covered with leather and two upright handles (pommels) near the center; held upright by two steel supports, one at each end
gymnastic horse: a padded gymnastic apparatus on legs

Other hypernyms of pommel horse include horse.

pommel horse (noun)	gymnastic horse (noun)
a gymnastic horse with a cylindrical body covered with leather and two upright handles (pommels) near the center; held upright by two steel supports, one at each end	a padded gymnastic apparatus on legs