Pending refers to purchase orders that have been created but have not yet been sent to the supplier.
These purchase orders can still be processed despite not being sent to the supplier.

Signed and Sent refers to Purchase Orders that have been either sent to the supplier or processed by Accounts. They can be accessed by clicking on the PDF icon.
If you are unable to open the PDF then this means this purchase order PDF was not sent to the supplier. It is likely the supplier was only supplied with your PO number. They have then sent an invoice with this PO number which has been processed by your accounts team.