A two way match compares the invoice with the purchase order and nothing else. What it proves is that the supplier billed what you agreed to buy, at the agreed price. What it assumes is that the goods arrived, because the document that would evidence that is not in the comparison. For services there is nothing to assume; for goods there is.
What it proves
Supplier, unit price, quantity and total agree with the order within tolerance. Price increases applied without notice, and quantities billed beyond what was ordered, are caught. That is genuinely useful and it is the complete control for anything that has no physical delivery to record.
What it assumes
That the delivery happened. An invoice for goods never sent agrees perfectly with the order, because the order describes what the supplier was asked to send. Only a record of what actually arrived separates the two cases, and a two way match is a decision to take that on trust.
Deciding rather than drifting
Configure the match by purchase category so goods get three-way and services get two-way. Then check periodically what share of goods invoices are being matched two-way. Drift towards two-way for goods is nearly always caused by receipts being hard to collect, and reviewing it turns an unexamined habit back into a decision.
Questions people ask about 2 way match
Is a 2 way match ever the right choice for goods?
As a knowing compromise where receipts genuinely cannot be collected, with the risk stated. Not as an unexamined default.
What replaces the receipt for services?
A confirmation from whoever commissioned the work that it was delivered, recorded against the invoice.
Does tolerance work the same way?
Yes. A percentage with an absolute cap, reviewed against the exceptions it actually produces.