money order vs order of payment

money order and order of payment both are nouns.

Word	Noun	Adjective	Verb	Adverb
money order	Yes	No	No	No
order of payment	Yes	No	No	No

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

money order: a written order for the payment of a sum to a named individual; obtainable and payable at a post office
order of payment: a document ordering the payment of money; drawn by one person or bank on another

Other hypernyms of money order include bill of exchange, draft.

money order (noun)	order of payment (noun)
a written order for the payment of a sum to a named individual; obtainable and payable at a post office	a document ordering the payment of money; drawn by one person or bank on another