HPS lamp voltage rises during life, while MH lamp voltage remains constant.
This is not always true, it depends on the fill composition and dosing, to what extend the fill components responsible for the arc voltage are operating at unsaturated vs saturated pressure.
Definitely the arctube gets hotter as the lamp ages. If saturated behavior dominates, the lamp then behaves very similar to HPS.
E.g. ceramic operate still quite big liquid salt pool, rhose components for sure operate at saturated vapor (still dunno how far these influence the arc voltage).