Headspace comparators are great tools for those looking to build the most precise ammunition.
That's a case gauge, not a headspace comparator.
New Starline Grendel brass is sized at the factory but it can have dings/etc, especially in the neck, from shipping/handling since it left the factory. I usual run it through my full length sizing die which is set to move the shoulder of fired cases back a few thousandths (.003"). It doesn't do any shoulder bumping on new brass, but it does straighten out the necks.
When you chambered rounds made with new brass, it is likely that the force of chambering was enough to overcome whatever was causing it to hang up in the case gauge.
The unsized/not adequately sized previously fired reload looks looks like it is near the SAAMI max chamber headspace dimension. So that's roughly what your chamber dimension is, except your chamber is slightly less because when the bolt on a semiauto unlocks there is still some pressure in the chamber, so the brass is expanded slightly longer than the chamber. Thus the need to "bump the shoulder back" at least a few thousandths for a semiauto to cycle reliably.
When you resized in accordance with the die setup instructions, you ended up near the SAAMI minimum.
So if you don't use a headspace comparator to set up your sizing die, your brass will get stretched from about SAAMI min to about SAAMI max (i.e. about 10 thousandths) every cycle. With a headspace comparator you can set it up so you are only moving the shoulder back a few thousandths from it's fired dimension every cycle. This can help extend brass life. However, these rounds may not chamber in someone else's rifle that has a shorter chamber.
Below is a picture of a headspace comparator. It is used with your calipers to make comparison measurements between fired and unfired brass headspace. Because the point where the comparator inset touches the shoulder is likely NOT exactly where official headspace is measured for a given cartridge, the actual numbers are meaningless except as a comparison. Popular headspace comparator kits are made by Hornady and Sinclair. Each kit has inserts that cover most bottleneck cartridges that are typically reloaded.
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