Two way invoice matching compares the supplier invoice against the purchase order and nothing else. Where nothing physical is delivered there is no third document to compare, so this is simply the complete control. Where goods are involved it leaves out the only routine evidence that anything arrived, which is a different situation entirely.
The purchases it fits
Professional fees, subscriptions, licences, rent, insurance, maintenance contracts, utilities. None produce a delivery anybody can record, so the comparison is necessarily invoice against order. What should accompany it is a confirmation from whoever commissioned the work that it was delivered, recorded separately from the approval.
The purchases it does not fit
Anything physical. Without a receipt, an invoice for goods that never arrived is indistinguishable from one for goods that did, and no amount of comparing price and quantity against the order changes that. Using two-way matching for goods is accepting a specific risk, and it should be a stated decision.
Configuring it properly
By purchase category rather than globally, so goods get three-way and services get two-way automatically. Reviewing what proportion of goods invoices are being matched two-way, and why, catches the drift that happens when receipts prove hard to collect and nobody quite decides to stop requiring them.
Questions people ask about 2 way invoice matching
Is two-way faster?
Marginally, and speed is not the reason to use it. The reason is that some purchases genuinely have nothing to receipt.
What confirms delivery for services?
A statement from whoever commissioned the work that it was done, recorded against the invoice and distinguishable from the spend approval.
Can we mix both?
You should. Which match applies is a property of what was bought, not a system-wide setting.