Just to clarify what the wheel thing is, I attach two photos of a Variotram wheel. This wheel is badly worn but does demonstrate the profile reasonably accurately. (Motor bogie, ex 2106, never repaired after the derailment, now part of the spares pool for 2107)
The wheels on the IWLR CAF cars look much the same.
The two major things from a 'plain' tram wheel - a tram wheel generally has less 'coning' and would be flatter on the running face. Tram-train wheels have a steeper angle to promote stability at speed with less flange strike when running on the railway. (which often have canted rails, whereas tram rails are laid flat to the road surface.)
The flange itself is a bit deeper/taller than a typical tram flange, but the thickness is typical. (but not for 'traditional Sydney' which ran rather thin flanges)
The real 'magic' happens on the wheel back. Notice the step. This step is for the railway point check-rails. It is high enough that on-street tracks it plays no part at all. (unless you happen to be running traditional Sydney tramway points which had raised check-rails instead of being totally flat as per normal tramway practice!). A normal tram wheel would run straight up from the flange back without the noticeable thickening and step.
This wheel would have no problems running around Melbourne unmodified.
Whereas a tram without this 'step', running on a 'heavy railway' would have to negotiate every set of points with extreme care lest a wheel jumps up and out of a points frog. Back in the days of yore when transferring Sydney tram cars from Kogarah or Strathfield (or even North Sydney) over the railway, the transfer crew carried special plates they would drop over each point frog they came to, to ensure the thin tramway flanges would go the right way and not derail.
The department though this so time-consuming and annoying they eventually built 'The Lizard' a road transporter trailer for tramcars, that in its day was the highest technology in road transport of the time.
One solution I saw used in France where a section of the tramway was shared with a heavy rail ndustrial siding is moveable frog points - so there can be no confusion at the crossing which way the flange should go for either profile.