That nice DB series 101 engine could be a tram by my reckoning if it was uncoupled, just like Toby the Tram from the Railway Series, no problem with Toby type engines being trams. However, with the exposed bogie wheels on the coupled passenger cars, it's a train at that point, even if a tram pulls it (or a horse or anything).
The Docklands Light Railway's vehicles are another one I thought of, they are often called trains, but I see no reasoning at all why they are more "trainy" than the trams at Rotherham?
I think the supreme court should rule on this important matter to clarify what exactly makes a tram.
Edit: I know street running doesn't happen on the DLR which some will argue is the reason, but neither does street running occur on other tramways such as Blackpool North Pier Tramway, Shipley Glen Tramway, or Scarborough Central Tramway etc. The vehicles and not the route is what counts.