allspice vs spice tree

allspice and spice tree both are nouns.

Word	Noun	Adjective	Verb	Adverb
allspice	Yes	No	No	No
spice tree	Yes	No	No	No

As nouns, spice tree is a hypernym of allspice; that is, spice tree is a word with a broader meaning than allspice:

allspice (noun)	spice tree (noun)
ground dried berrylike fruit of a West Indian allspice tree; suggesting combined flavors of cinnamon and nutmeg and cloves	tree bearing aromatic bark or berries
aromatic West Indian tree that produces allspice berries	Pacific coast tree having aromatic foliage and small umbellate flowers followed by olivelike fruit; yields a hard tough wood
deciduous shrubs having aromatic bark; eastern China; southwestern and eastern United States