Are polyurethane and white Styrofoam one and the same?

Not quite.

Polyurethane features superior thermal insulation with a factor of RSI: 2.8 (R:16). In addition, since polyurethane adheres better to door surfaces, it provides twice as much resistance to flexion as polystyrene (Styrofoam) in a comparable door. Entrance doors are also insulated with polyurethane foam. Polystyrene is the material used to make coffee cups.