Yes, confusing isn't it? A product of the marketing people I suspect.
An electric shower takes water from the main cold water feed and heats it instantaneously for you. The pressure comes from the mains pressure. It is a very simple device inside.
A power shower has hot and cold water feeds, taken from the cold water tank in the roofspace, and contains a mixer valve (often thermostatically controlled). It also has an electrical pump to boost the pressure of the water.
The Triton you have is an electric shower. Many of the electric showers are desrcibed as having 'power control' or some other meaningless term.