You can run one stick of DDR2 memory alone, and it will work, but you can't run one stick of DDR2 and one stick of DDR together. While there are motherboards that have DDR and DDR2 slots on the same motherboard, I believe you can't use both types at the same time.
Just the speeds they run at and how many pins they have is basically it. DDR3 runs faster than DDR2 or DDR. DDR2 runs faster than DDR. DDR is faster than PC 133.