Do the modes all use different amounts of fuel because I live in Eco on the dash but the radio has Race on it?
The car will use as much fuel as your right foot allows
It's easier to use fuel in Sport/Race due to the gears being held longer, but in reality that can be all but negated with careful throttle control.
On a related note, in case anyone was still under the impression that the Think Blue trainer was anything other than nonsense, for DSG users, drive at 70mph, on ACC, with the engine in Normal (D on the gauges) and look at your think blue score. Then change to Sport by pulling back on the gear lever, switch up if necessary to top gear again, and watch the scores drop right down despite using no more fuel