red deer vs elk

red deer and elk both are nouns.

Word	Noun	Adjective	Verb	Adverb
red deer	Yes	No	No	No
elk	Yes	No	No	No

As nouns, red deer and elk are synonyms defined as:

Other synonyms of red deer include American elk, Cervus elaphus, wapiti.

red deer (noun)	elk (noun)
common deer of temperate Europe and Asia	large northern deer with enormous flattened antlers in the male; called `elk' in Europe and `moose' in North America
	common deer of temperate Europe and Asia
	large North American deer with large much-branched antlers in the male