NRA and USRA revolver matches were/are shot at 50 yards and 25 yards (mid range). At one time full-power .38 Spl. wad-cutter ammunition was loaded with 158 gr. wad-cutter bullets at standard velocity of ca. 850 FPS. this cartridge was used for shooting the 50 yard stages. For the 25 yard stages a second load, a 148 gr. wad-cutter at a reduced velocity of 770 FPS was developed. The purpose was that the two cartridges would be used at the respective distances and would have the same point-of-impact at their range. Naturally the 148 gr. load was designated as "Mid-Range" since that was the distance it was intended for, just as simple as that. The Mid-Range load was found to be the more accurate and shooters simply used it at both distances and adjusted their sights accordingly, or had 2 guns sighted for each distance.
I believe the full-charge 158 gr, wad-cutter fell out of use and was discontinued sometime in the 1920s. The "Mid-Range" designation for the 148 gr. load has continued to be used to this day in spite of the fact that virtually no one knows the reason for the term anymore!