royal stag vs royal

royal stag and royal both are nouns.

Word	Noun	Adjective	Verb	Adverb
royal stag	Yes	No	No	No
royal	Yes	Yes	No	No

As nouns, royal stag and royal are synonyms defined as:

royal stag (noun)	royal (noun)
stag with antlers of 12 or more branches	stag with antlers of 12 or more branches
	a sail set next above the topgallant on a royal mast

royal stag (adjective)	royal (adjective)
	of or relating to or indicative of or issued or performed by a king or queen or other monarch
	established or chartered or authorized by royalty
	invested with royal power as symbolized by a crown
	being of the rank of a monarch
	belonging to or befitting a supreme ruler