An invoice and a purchase order describe the same transaction and are written by different parties at different moments for different purposes. The order is the buyer stating what they agreed to buy, in advance. The invoice is the supplier claiming payment, afterwards. Everything payables does with the pair follows from that asymmetry.
Written by the buyer, before
The order lists items, quantities, prices, a delivery date and your terms, and carries a unique number. It records the agreement and creates the commitment once the supplier acts on it, which is why approval belongs before it goes out. It is your evidence of what was agreed, and it is only as good as the care taken over it.
Written by the supplier, after
The invoice states what was supplied, what is owed and by when, with their own reference and, ideally, your order number. It is a claim rather than a fact, which is the mental shift that distinguishes business payables from consumer payment. Claims are verified before they are settled.
The document that decides between them
The goods receipt. An order and an invoice agreeing proves the supplier billed what you asked for; it proves nothing about delivery. Only a record of what arrived closes that gap, which is why the standard control for goods compares three documents rather than two.
Questions people ask about invoice vs purchase order
Which comes first?
The order, always, where one exists. An order raised after an invoice arrives is documentation rather than a control.
Can they legitimately differ?
Yes: freight added at billing, tax, partial deliveries invoiced separately, and agreed price changes. Tolerance and dated revisions handle those.
What if there is no order?
The invoice is approved on its own merits by whoever authorised the spend, which is the most expensive path through payables.