order Piperales vs plant order

order Piperales and plant order both are nouns.

Word	Noun	Adjective	Verb	Adverb
order Piperales	Yes	No	No	No
plant order	Yes	No	No	No

As nouns, plant order is a hypernym of order Piperales; that is, plant order is a word with a broader meaning than order Piperales:

order Piperales (noun)	plant order (noun)
Piperaceae, Saururaceae, Chloranthaceae	the order of plants