white cedar vs arborvitae

white cedar and arborvitae both are nouns.

Word	Noun	Adjective	Verb	Adverb
white cedar	Yes	No	No	No
arborvitae	Yes	No	No	No

As nouns, arborvitae is a hypernym of white cedar; that is, arborvitae is a word with a broader meaning than white cedar:

white cedar: small evergreen of eastern North America having tiny scalelike leaves on flattened branchlets
arborvitae: any of several Asian and North American conifers of the genera Thuja and Thujopsis

white cedar (noun)	arborvitae (noun)
slow-growing medium-sized cedar of east coast of the United States; resembles American arborvitae	any of several Asian and North American conifers of the genera Thuja and Thujopsis
small evergreen of eastern North America having tiny scalelike leaves on flattened branchlets