The "starter" and "starter motor" are not exactly the same thing, but they're close enough that people might use the two terms interchangeably. Technically your starter motor is an electric motor which forces the gas engine to move until it can fire and run on its own. The starter is the entire system that makes your car start - it includes the starter motor, a solenoid to connect electric power to that motor, a drive gear to connect the motor to the engine, and all the wires & electrical components necessary to make the whole thing work.
But most of the time if someone just casually mentions the car's "starter" they are talking about the electric motor.
I agree with what other's have said: before you run out and spend money on a new starter motor, get the battery checked more thoroughly. Car batteries tend to die slowly and may be operating at less than peak performance for months or even years before they die completely. Most auto part's stores or repair shops can test the battery under a load to see if its working. You can also try charging the battery if you have a charger, or try jump-starting the car. Or swap batteries with another vehicle to see whether its the battery or the starter.
Anyway, its very common that a battery will still output 12 volts on a volt-meter and can power the car's accessories such as lights and radio, but cannot produce enough amperage to spin the starter motor. The radio might draw 5-10 amps while the starter can easily draw 200+ amps.
Bottom line is that I'd spend more time on checking the battery before I would spend a penny on the starter.