Two way matching answers one question well and another not at all. It confirms that the supplier has billed what you agreed to buy, at the price you agreed. It says nothing about whether the goods arrived, because the document that would answer that, the goods receipt, is not in the comparison. That division is the whole of it.
What it confirms
Supplier, unit price, quantity and total against the purchase order, within tolerance. Where a price has moved without notice, or a quantity has been billed beyond what was ordered, this catches it. That is genuinely useful and it is why two-way matching is the complete control for anything that has no physical delivery.
What it cannot confirm
That anything was delivered. An invoice for goods that never arrived agrees perfectly with the order, because the order is what the supplier was told to send. Only a record of what actually arrived distinguishes the two cases, and that is the document two-way matching leaves out.
How to use it deliberately
Apply it by purchase category rather than globally: services and subscriptions two-way, goods three-way. Then check periodically what proportion of goods invoices are being matched two-way and why. That proportion is where the drift shows, and drift here is almost always caused by receipts being hard to collect rather than by a decision.
Questions people ask about 2 way matching
Is two way matching common?
Very, and appropriately so for services. It becomes a problem when it quietly becomes the default for goods as well.
What confirms a service was delivered?
A statement from whoever commissioned it, recorded against the invoice and distinguishable from the spend approval.
Does tolerance work the same way?
Yes: a percentage with an absolute cap, reviewed against the exceptions it actually produces.