All the Eureka canisters that take the Style "H" bags are called Princesses, even the "turtle shell" version! So the brandywine version at the start of this thread is definitely a Princess (it seems to be missing the little foot pedal over the power switch).
There is a deluxe Princess called the "Prince" which is similar in shape, but it seems to have a more advanced motor - I think something about a twin-fan or something like that.