bay-rum tree vs wild cinnamon

bay-rum tree and wild cinnamon both are nouns.

Word	Noun	Adjective	Verb	Adverb
bay-rum tree	Yes	No	No	No
wild cinnamon	Yes	No	No	No

As nouns, bay-rum tree and wild cinnamon are synonyms defined as:

Other synonyms of bay-rum tree include bayberry, Jamaica bayberry, Pimenta acris.

bay-rum tree (noun)	wild cinnamon (noun)
West Indian tree; source of bay rum	large evergreen shrub or small tree having white aromatic bark and leathery leaves and small purple to red flowers in terminal cymes
	West Indian tree; source of bay rum