Most exchanges are now batching transactions, and the average transaction has more than one input and output. Should those be counted as separate transactions, or do we count 100 addresses that receive Bitcoin in one txid as one transaction?
Since it is easier to count transactions in a block rather than counting outputs while ignoring change output, every time the rate is reported it is counting transactions. But you are right, technically when talking about "throughput" we should count payments not transactions and one tx can contain multiple payments.