The gauges are driven by stepper motors with the needles just pushed on them. You could fix that 3 mph difference by just popping the needle off and repositioning it. The digital reading is the value the computer is sending to the gauge.
There is no direct connection between the Mustang gauges and any of the sensors. The computer reads the values from the sensors and then sends the inputs to the gauges. Since the gauges are zero'd as you turn on the ignition (watch them flip back and forth), there is a mechanical aspect to making them match the computer input. When stepper motors begin to fail they don't find the right zero point and the readings go way off. This was a common failure on earlier Mustangs.