A purchase order and an invoice describe the same transaction from opposite ends and at different times. The order is your statement of what you agreed to buy; the invoice is the supplier's claim for payment for it. What joins them in practice is a reference number, and what makes the join trustworthy is a record of what actually arrived in between.
The reference is the join
The order number quoted on the invoice is what lets the two documents be brought together automatically. Without it, an invoice is an isolated claim and somebody has to establish what it relates to, which is research rather than checking. This is why payables asks suppliers to quote it and why organisations return invoices that do not.
The receipt makes the join trustworthy
An order and an invoice agreeing tells you the supplier billed what you asked for. It does not tell you anything arrived. The goods receipt is what closes that gap, and it is why the standard control for goods compares three documents rather than two. Without it you are trusting the invoice on the point that matters most.
Where they legitimately differ
Freight added at billing, taxes, partial deliveries invoiced separately, and price changes agreed after the order was raised. All normal. Tolerance is what lets small differences pass and revisions are what record agreed changes, and between them they keep the exception queue for genuine disagreements.
Questions people ask about purchase order and invoice
Should an invoice always quote an order number?
Where you raised an order, yes, and most suppliers will comply because it speeds up their own collection.
What if the invoice total differs from the order?
Within tolerance it clears; outside it, it becomes an exception with a reason and goes to whoever can resolve it.
Can one order cover several invoices?
Yes, commonly, for staged deliveries or ongoing services. That is why line-level matching with running quantities matters.