I usually use “backing up” a turn to mean that a driver is entering the turn too aggressively/too fast and has to scrub speed later or wait to get back onto the power longer than they should be.
I see it a lot with drivers moving from a 2-stroke to a 206. The team I coached for most of this racing season was primarily 206 drivers, and a few of them jumped in from Swift or KA. Getting into a 206 means that you need to get onto the power earlier with the low horsepower and high-stall clutch, and a lot of these drivers were driving more like a 2 stroke. So when I said “you need to back the corner up” I would make sure they understand that means braking earlier to accelerate sooner through the corner, and possibly turn in earlier as well.
Regarding racing in a pack or behind another driver, braking early to not run into the back of the driver is an okay practice, but sometimes results in a driver under-driving the corner. I will say that a lot of drivers tend to try braking later and turning in earlier when following someone because they see themselves gaining on entry but lose all that momentum at the exit. I’ll then remind drivers to back up the corner when following someone, but that’s really more of a band-aid for a driver that struggles to look “through” a driver to their markers when following.
So to me, “backing up” a corner is more to do with driving pace than driving behind a competitor. Braking earlier when following a pack, whether it’s to not hit the driver in front of them or get a better exit to make a pass into the next corner, is more of a racecraft discussion where I’ll use a different term to keep from confusing them.
I also primarily worked with cadets and juniors this year though, so I would expect you to understand that difference more than my 7-year-old Micro driver.