bay-rum tree vs bayberry

bay-rum tree and bayberry both are nouns.

Word	Noun	Adjective	Verb	Adverb
bay-rum tree	Yes	No	No	No
bayberry	Yes	No	No	No

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

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

bay-rum tree (noun)	bayberry (noun)
West Indian tree; source of bay rum	West Indian tree; source of bay rum
	deciduous aromatic shrub of eastern North America with grey-green wax-coated berries