The procure to pay cycle is an operational process that touches the accounting records at three specific moments, and knowing which they are explains why finance cares about steps that look purely administrative. A purchase order is not an accounting entry. A goods receipt often is. The invoice certainly is, and so is the payment.
The order: a commitment, not an entry
Raising a purchase order commits the organisation but does not usually create a ledger entry. It matters to accounting as a commitment for budgeting and forecasting, which is why the open-order report is useful to finance as well as to purchasing. What it is not is a transaction, and treating it as one confuses the picture.
The receipt: usually the accrual
Goods received and not yet invoiced are an obligation, and this is where the goods-received accrual comes from. That makes the receipt an accounting-relevant act performed by operational staff who do not think of it that way, which is exactly why it gets skipped. The received-but-not-invoiced report is the accrual in operational form.
The invoice and the payment
The invoice posting records the liability and the cost, coded to an account and a cost centre. The payment settles it. Which period each belongs in, and how any particular item should be treated, is your accountant's judgement; producing accurate, timely underlying detail is payables' contribution to getting it right.
Questions people ask about p2p accounting
Why does finance care about goods receipts?
Because they are the basis of the accrual for goods received but not invoiced. Missing receipts mean an accrual built by estimate rather than by record.
When should an invoice be posted?
That is an accounting policy question about cut-off and approval status. The operational requirement is that the underlying detail and dates are accurate.
Does the purchase order affect the accounts?
Not usually as an entry, but as a commitment it informs budgeting and forecasting, which is why open-order reporting has an audience in finance.