saddle horse vs Arabian

saddle horse and Arabian both are nouns.

Word	Noun	Adjective	Verb	Adverb
saddle horse	Yes	No	No	No
Arabian	Yes	Yes	No	No

As nouns, Arabian is a hyponym of saddle horse; that is, Arabian is a word with a more specific, narrower meaning than saddle horse:

saddle horse (noun)	Arabian (noun)
a lightweight horse kept for riding only	a spirited graceful and intelligent riding horse native to Arabia
	a member of a Semitic people originally from the Arabian peninsula and surrounding territories who speaks Arabic and who inhabits much of the Middle East and northern Africa

saddle horse (adjective)	Arabian (adjective)
	of or relating to Arabian horses
	relating to or associated with Arabia or its people