The above explanations are consistent with my observations as well; lower pressure loads are more susceptible to sooty cases while upper to max loads seem to come out clean.
You can use this explanation of cartridge case expansion as you describe for her these (super simplified) steps in firing and then reloading:
The loaded round taken from the factory box consists of a cartridge case, primer, powder and bullet. This round is sized to fit within the chamber of the firearm, allowing the round to be inserted for firing.
Upon firing, the primer is struck. A pressure-sensitive compound ignites, causing a flame to shoot into the cartridge case which ignites the powder charge.
The gunpowder burns extremely quickly, turning from solid to gas which greatly spikes pressure within the case.
Under increasing pressure, the cartridge case expands slightly, hugging the walls of the chamber as the building pressure begins pushing the bullet out of the case. The cartridge case mouth forms a seal against the building pressure, so the ever expanding gasses can only head down the barrel behind the moving bullet and out the muzzle (the intended exit).
With lighter loads this seal is not as complete as with higher pressure loads, allowing a touch of gas leakage causing the soot/staining you see on the outside of the cases.
Once the bullet is clear of the case and is moving out the barrel the pressure drops dramatically, allowing the walls of the cartridge case to contract slightly.
This bit of contraction allows for extraction, so the fired cartridge case may be removed from the chamber allowing a fresh one to be loaded back into the chamber (if so desired).
The expended cartridge case remains slightly expanded after firing. This allows for a bullet to be inserted into the cartridge case but then it falls out. So to be reused, it must be resized back down.
When you are reloading, you are first kicking out the spent primer and, under the pressure exerted by the sizing die, you are squeezing the resilient brass cartridge case back down to a size that will allow it to hold a bullet firmly and be chambered again.
You then reinsert a primer, add powder, (sometimes) flare the case mouth a bit, you set a bullet at the case mouth and then you use a die that holds the bullet in place as the bullet is pressed back into the neck of the cartridge case.
It is then either left as-is and held securely by the tension of the fit (neck tension) or a crimp (squeeze) is applied with a crimping step to increase the tension to hold the bullet in place with greater force. The resulting crimp may be along the walls of the cartridge case, at the mouth of the cartridge case, or a combination of both.
You then are ready to fire it again.
Again, this is super simplified but it may help to explain the steps you’re doing together at the reloading bench as she creates her own rounds to shoot
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Stay safe.
