A typical transistor
switches an electrical signal, and can be extremely small, and usually is part of an integrated circuit
A power transistor is typically in a module of its own,
and is the size of a nickel or larger. The power transistor, as the name implies, switches not just a signal,
but power; the typical transistor deals with miliamps of
power, where the power transistor may deal with 2 amps or more. Because of the large amount of power,
frequently a heat sink is also needed.
Power transistors are used to convert miliamp level signals
into enough power to actuate a physical device, such as
a motor or solinoid or other actuator.
Power transistors are also a major component of switching power supplies. If your power supply stops
working, the most likely failed component is the power transistors. (Although the fan fails more often, this is not
the immediate death of the power supply.)