A two way match compares the supplier invoice against the purchase order and nothing else. For services and anything without a physical delivery it is the correct control, because there is no receipt to be had. For goods it is a compromise, and organisations often arrive at it because receipts were hard to collect rather than because it was the right choice.
Where it is correct
Professional fees, subscriptions, rent, software, maintenance contracts and consultancy. None of these produce a delivery anybody can record, so the comparison is necessarily between the invoice and what was agreed. What should accompany it is a confirmation from whoever commissioned the work that it was actually delivered, which is the functional equivalent of a receipt.
Where it is a compromise
Physical goods. Without a receipt nothing in the routine process evidences that a delivery happened, so an invoice for goods that never arrived is indistinguishable from one for goods that did. Using two-way matching here is accepting that risk, and it deserves to be a stated decision rather than an accident of implementation.
How to run it well
Compare supplier, price and total against the order, and require a separate confirmation of delivery or completion from the person who commissioned it. Keep that confirmation distinguishable from the approval on the record, because confirming that work happened and authorising the spend are different assertions made for different reasons.
Questions people ask about two way match accounts payable
Is a two way match enough for an auditor?
For services it is standard. For goods, expect to be asked how delivery is evidenced, and have an answer that is not simply that nobody records it.
Can matching differ by category?
Yes and it should. Which match applies is a property of what was bought, not a system-wide setting.
What replaces the receipt for services?
A confirmation from whoever commissioned the work, recorded against the invoice.