We always called that a "tactical reload," with an "emergency reload" occurring when your slide locked back on an empty mag (hence the emergency). I sometimes add a round, sometimes not. Usually, it's when I was training and knew I needed one more to avoid a reload in the fire string. As for carry, eh. Sometimes I'll do what others have suggested and replace the mag with a full mag, usually with a 1911 or my Glock 43. Not so much with the 19X . . .
I have always thought an administrative reload involved replacing a partially empty magazine with a fresh full magazine while retaining the partial magazine in case you need it. Usually done while behind cover in a gunfight. I've generally considered a tactical reload to mean you've run the gun dry, drop the empty mag, insert a full mag, cycle the gun and continue shooting. But maybe my labels are wrong.
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