As with many PTE areas, the PlusBus ticket covers a massive area, and the website is correct that both are functionally identical. The ticket office is wrong - they should have checked the website if they weren't sure, claiming railcards aren't valid and that the only map would be at Stockport station is completely insane.
Unfortunately, the setup of PlusBus fares is not how I would have done it, and doesn't help with causing confusion here (though, it doesn't excuse a lot of the nonsense that was spouted). Stations within the zone get their own PlusBus code with a name of [station]+Bus (with a fare from [station] to this location code defined), so you end up with lots of tickets that say different things that actually mean the same thing. Even worse, smaller stations don't get the PlusBus ticket defined at all because the NLC codes needed for this are in short supply, so when when there's a small station in a big zone that'll sell basically none of them it just doesn't get setup - a pragmatic ticket office will probably sell you a PlusBus from one of the big stations, but that doesn't help when you're buying online.
My personal view here is that there should be be location code per PlusBus zone with a sensible descriptive name (perhaps Greater Manchester+Bus in this case). Then you can define fares from all stations in the zone to this one location so it gets automatically retailed online for every single station in the zone, you have no issue with using excess scarce codes, there is one name for ticket offices and bus drivers to remember so they don't get confused by "we aren't in Stockport".
That is however, now where we are, so in your position I would be sending a complaint to the bus company in question (including asking for a refund if you had to pay a cash fare), and a complaint to whoever runs the ticket office at Picadilly. If it was an eTicket and you scanned the barcode and it rejected on the bus, it would be interesting to know a bit more about the operator of the bus in question, and who you bought your PlusBus ticket from.