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I don't think that anything but confusion will result from defining any acronym that begins with a "C" as the distance from the cartridge head to the point on the bullet that is anything different than its tip.
Measurements with bullet comparators are useful FOR INDIVIDUAL RIFLES, but not as standards, because bullet contact with the rifling can occur at much different locations on the bullet, depending on how the beginning of the rifling is shaped with respect to how the bullet is shaped. And, the beginning of the rifling will erode over time, changing that relationship.
So, if you think that using a comparator to measure the distance from the case head to the beginning of the full-diameter part of the bullet is giving you the distance that will allow your bullet to just touch the rifling, you are probably misleading yourself by some unkown amount. On the other hand, if you use the gun itself to determine that distance, you will have a measurement that is useful FOR THAT GUN ONLY. Finding the measurement that YOUR bullet comparator gives you with a cartridge made-up with a particular bullet that just touches the lands will give you an easy way to monitor your ammo as it is produced, so there is some value in using a comparator.
But, there seems to be little value to us forum members swapping those particular length measurements. What we should swap is the DISTANCE OFF THE LANDS, which is often just called "bullet jump". That seems to have the most meaning with respect to peak pressure and accuracy, although matching it from gun to gun is not any guarantee for matching either peak pressure or accuracy from gun to gun.
SL1
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