A "money order" is issued, as you say, by a bank or post office. You present cash to them and they issue a piece of paper payable to a third party. This is used as an alternative to sending cash in the mail. Or when a person does not have a personal checking account. Or when the company to be paid does not accept personal checks. They want a guaranteed payment.
A "Purchase Order(PO)" is what a company issues to another company as the commitment to buy items or services. If I make widgets, your company may give me a PO for 500 widgets. I would then ship them to you and send you an invoice, which is a demand for payment. You would then have to pay me.