pole horse vs trotting horse

pole horse and trotting horse both are nouns.

Word	Noun	Adjective	Verb	Adverb
pole horse	Yes	No	No	No
trotting horse	Yes	No	No	No

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

pole horse: the horse having a starting position next to the inside rail in a harness race
trotting horse: a horse trained to trot; especially a horse trained for harness racing

Other hypernyms of pole horse include trotter.

pole horse (noun)	trotting horse (noun)
a draft horse harnessed alongside the shaft or pole of a vehicle	a horse trained to trot; especially a horse trained for harness racing
the horse having a starting position next to the inside rail in a harness race