Tom,
The small cylindrical device on top of your starter is the "starter solenoid". Let me copy some text from
http://www.howstuffworks.com/ :
Starting system
The starting system consists of an electric starter motor and a starter solenoid. When you turn the ignition key, the starter motor spins the engine a few revolutions so that the combustion process can start. It takes a powerful motor to spin a cold engine. The starter motor must overcome:
All of the internal friction caused by the piston rings
The compression pressure of any cylinder(s) that happens to be in the compression stroke
The energy needed to open and close valves with the camshaft
All of the "other" things directly attached to the engine, like the water pump, oil pump, alternator, etc.
Because so much energy is needed and because a car uses a 12-volt electrical system, hundreds of amps of electricity must flow into the starter motor. The starter solenoid is essentially a large electronic switch that can handle that much current. When you turn the ignition key, it activates the solenoid to power the motor.
The mechanical switch (which is what is on your other starter) is simply an on/off switch that is activated by the foot pedal. It simply closes the circuit to feed your battery's 12 volts to the starter motor.
I think you might be able to simply swap the two, but I will defer to those who have done it.
