bill-me order vs purchase order

bill-me order and purchase order both are nouns.

Word	Noun	Adjective	Verb	Adverb
bill-me order	Yes	No	No	No
purchase order	Yes	No	No	No

As nouns, purchase order is a hypernym of bill-me order; that is, purchase order is a word with a broader meaning than bill-me order:

bill-me order: an order that is received without payment; requires billing at a later date
purchase order: a commercial document used to request someone to supply something in return for payment and providing specifications and quantities

Other hypernyms of bill-me order include order.

bill-me order (noun)	purchase order (noun)
an order that is received without payment; requires billing at a later date	a commercial document used to request someone to supply something in return for payment and providing specifications and quantities