Many of these terms are used interchangeably however we usually try to inquire to ensure the correct service is being carried out. Mileage correction and Odometer correction are essentially the same service. Sometimes one might refer to it as a correction, calibration, programming, or repair. However, if "repairs" are used by someone, we as techs need to confirm whether someone might need an odometer correction or simply the LCD repaired that shows the mileage.
If repairs are needed, we will check on our end if this cluster is supported for repairs and specifically that we can fix the LCD not working on it. To summarize, if one requests a numeric change of the odometer value, this is what we refer to as a mileage correction.