elk vs red deer

elk and red deer both are nouns.

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

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

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

elk (noun)	red deer (noun)
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
common deer of temperate Europe and Asia
large North American deer with large much-branched antlers in the male