Hi Rosemary-
From the situation you've described, I think it really all depends on the timing of everything and what happened to the inventory.
If the inventory was all sold off or used in some way, then you'd need to get that inventory back (a SOP return if sold through sales, for example). Then you'd use "Inventory with Credit" to get it back out to the vendor and put a credit memo in AP. If you checked the box to Replace Returned Goods, this would create a new PO to receive anything from the vendor.
If the inventory was received and matched, but never used, it would be Return with Credit. That will get the inventory out and create a credit memo in AP. If you checked the Replace Returned Goods box, there would be a new PO created to the vendor since the PO was in history. If you checked the Replace Returned Goods box and the PO was still in the open files, it would just reopen the PO and that particular line item so you could receive on it again.
The other two return types (Return and Inventory) don't create a credit memo. They're just used to back something out in the case of posting a shipment transaction wrong (return) or return inventory to a vendor (inventory) that has previously been used and then received back somehow to your own inventory.
I hope this helps.
Thank you.
Joe