The approver is the person who is authorized (by value of the PO usually) to signoff on the purchase.  Many companies have authorization limits that escalate as the size of the PO goes up or the type of purchase (inventory vs expense vs capital, etc).

The confirmer (at least in my experience) is the person who updates the PO with the confirmation from the supplier.  This usually involves matching the date, quantity, price and other possible aspects of the PO to confirm the supplier has agreed to the purchase order contents and timeframe.