post oak vs oak tree

post oak and oak tree both are nouns.

Word	Noun	Adjective	Verb	Adverb
post oak	Yes	No	No	No
oak tree	Yes	No	No	No

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

post oak: small deciduous tree of eastern and central United States having dark green lyrate pinnatifid leaves and tough moisture-resistant wood used especially for fence posts
oak tree: a deciduous tree of the genus Quercus; has acorns and lobed leaves

Other hypernyms of post oak include oak.

post oak (noun)	oak tree (noun)
small deciduous tree of eastern and central United States having dark green lyrate pinnatifid leaves and tough moisture-resistant wood used especially for fence posts	a deciduous tree of the genus Quercus; has acorns and lobed leaves