Difference between Ground and Digital Ground
Digital Ground usually refers to the reference voltage of digital logic ICs. This means that no analog signals are coupled into this reference plane.

You can often see analog and digital ground where digital ground will be the reference for any logic and analog ground will be the return path for any analog circuits.

Imagine an Atmel AT32UC3C. It has both an analog and a digital ground. The analog ground is intended as reference voltage for the ADCs and DACs or Analog Compare interfaces whereas all other logic is considered to be digital.

You will also often see that analog and digital ground are connected to each other directly or via a ferrite. "Ground" is just a name for the reference net in your circuit.

The main reason for having multiple (different) grounds is that effects of one application do not affect the other (e.g. analog vs. digital).