All i will add is be very careful with tuning boxes as most of them just increase the rail pressure as said by many others and that is not going to give you the best results......Get a decent remap, i would probably use Celtic Tuning as they are reputable and mobile but its up to you. The results on a C220 CDI will be very good, for comparisons sake, the car will be marginally quicker than a standard C270 CDI with very similar outputs but will feel a bit livelier and more responsive. Go for the remap you wont be disappointed!! Its the best value mod on a diesel....imo
Another reason that it saves on fuel, as well as the fact you have a cleaner more efficient burn, is because you have more torque so in certain situations where the car would previously have changed down a gear to accelerate (like when overtaking) it now doesnt need to as the torque output is sufficient to stay 'in gear'......
Lastly, the difference between a chip and a remap can actually be nothing. The difference is simply that a remap is having the new map flashed to the cars existing ECU chip whereas a chip means to remove the cars current chip and replace it with a new one that has a new map on it. Basically the same result but nobody 'chips' cars anymore really unless its too old to be able to be remapped. In fact Superchips will remove one of their chips and refit an original one and then remap the car for free if you have one of their old superchips still on your car......