Are we quite sure a Traincard is captured by the 19c definition of a PTE product? As far as I know, they are not promoted or sold by System One which handles the sale of TfGM's season tickets, and they are valid at four stations which are not administered by a PTE. IIRC, West Yorkshire seasons that include zone 6 or 7 are not treated as PTE products.
You'll be surprised what the system one website doesn't promote (it's aimed primarily at bus travel). The "What is System One" webpage says....
What is System One?
System One offers DaySavers and Bus Savers for unlimited use on any bus in Greater Manchester. You can now buy the 'E-Bus Saver' range here.
System One Travel Limited (GMTL) is co-owned by Greater Manchesters private bus, rail and tram operators and Transport for Greater Manchester (TfGM).
System One offers a choice of one day, 7 day, 28 day or annual travelcards. All are featured on this website and we've indicated where you can buy them. Just click Find a travelcard for all the info you need.
You might note that all the tickets they offer have bus validity.
Anyway, the GM Traincard is in the PTE section of iKB and it doesn't have the usual season ticket period of validities (one week, one month and one year only).
The GM Countycard is also valid at some stations outside of the TfGM area (the same rail validity as the Traincard), is in the PTE section of iKB, and is valid for periods of one week, one month and one year.