Stepper and DC Motors? What's the diff?

For purposes of mobile robotics, there are basically 2 different types of motors;

• Stepper Motors - the stator windings are around the outside, there is a permanent magnet on the rotor. Electric current is repeatedly pulsed to windings to force the rotor to turn in steps.
  

• DC Motors - the magnets are on the outside and the electric windings are around the rotor.  Electricity is applied to the core electromagnet.

I'm no electrical engineer (as I will probably repeat many times in this blog), but after doing some research on the torque needed to drive the wheels (to calculate torque, you use the weight, angle of incline, and radius of drive wheel), I settled on using stepper motors. 

Coming from a computer science background, it seemed desirable to be able to control stepper motors precisely using software.   

Stepper motors also provide holding torque (torque when the motors are not turning), which I thought might be useful on stairs.