wild cinnamon vs bayberry

wild cinnamon and bayberry both are nouns.

Word	Noun	Adjective	Verb	Adverb
wild cinnamon	Yes	No	No	No
bayberry	Yes	No	No	No

As nouns, wild cinnamon and bayberry are synonyms defined as:

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

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