Towel rails and bathroom radiators are essentially the same and their names are often used interchangeably. They both serve the purpose of heating the bathroom.
However, towel rails are known for featuring a design element specifically to keep towels warm. This may be a ladder style construction or an overhanging rail to provide storage for towels.
Bathroom radiators may refer to any type of radiator that is installed in the bathroom. This is not limited to towel rails, but also may include horizontal and vertical radiators.
You can also turn a vertical bathroom radiator into a towel rail with additional accessories like detachable chrome towel hooks and rails.