A purchase order and an invoice describe the same transaction and are written by different parties at different times for different purposes. The order is the buyer saying what they agreed to buy, before anything happens. The invoice is the supplier claiming payment, after. Keeping that straight explains most of what payables does with the two documents.
Who writes each, and when
The buyer writes the order and sends it before delivery: items, quantities, prices, delivery date, terms. The supplier writes the invoice and sends it after supplying: the same items and quantities, plus tax, a due date and their own reference. The order comes first and the invoice should agree with it.
What each is for
The order records the agreement and creates the commitment, which is why approval belongs before it is issued. The invoice requests payment and starts the payment clock. The order is your evidence of what was agreed; the invoice is their claim about what should be paid, and the gap between the two is what the match examines.
Why the third document matters
An order and an invoice agreeing proves the supplier billed what you asked for. It proves nothing about delivery. The goods receipt closes that gap, which is why the standard control for physical goods compares three documents. Comparing only the order and the invoice trusts the supplier on precisely the point most worth checking.
Questions people ask about purchase order vs invoice
Can an invoice arrive without an order?
Frequently, and it then has to be approved on its own merits by whoever authorised the spend, which is the most expensive path.
Which document has the payment terms?
Both may. Terms on your order are what you rely on when the supplier's invoice states different ones, which is why including them matters.
Can one order produce several invoices?
Yes, for staged deliveries or ongoing services, which is why line-level matching with running quantities is worth having.