@RegionRat so the measurement with the hornady comparator should be called shoulder datum to case head? They just muddied the water by calling it a headspace gauge, which could be confused with a go/ no go gauge.
Sorry to be late getting back to you, but the others have already answered your questions pretty well I think.
Hornady does not call it a Head Space Gauge it called a Headspace Comparator. No confusion it compares before against after,
59FLH is on point.
Unfortunately, many times in open forums the terminology isn't held tight, but with a little forgiveness it can work in context and we figure out what folks mean without grammar-nazis getting spooled up.
Most of the folks who shoot and make great contributions to our sport are not formally trained gunsmiths or credentialed ballisticians. That means we all have to be careful to back each other up if the miss-use of language or technicalities risks taking us off track, but we also let it go when it doesn't get in the way of getting the points across.
There is only a slight chance this specific example of terminology will cause an issue since most of the time people figure out that these tools are only case comparators. If you ever buy what is called a GO Gage, you could use it to reference your comparator measurements against the Go Gage dimensions as well as evaluate new factory ammo shoulder datum dimensions compared to SAAMI specs. You can live happily without this by just comparing to your chambers.
You have already learned the diameters are just as important as the lengths, and they are often the cause of difficulty for beginners. The advice you got to check those diameters was on point.
BTW, now is a good time to get familiar with SAAMI Specs for your 30-06 chamber and cartridge. I will emphasize that those are two separate sets of dimensions, not just one. There are some SAAMI specs that are better than others and I never liked the allowable values on this one, but I would still encourage you to study them both so you understand cartridges and chambers, and more importantly how they relate to each other.
I think the others have done a pretty good job of clearing up your issues by this point.
You now realize that sizing is really simple in the way that a die has one only one degree of adjustment, yet is complex when you run into the subtleties of the relationship to your chambers and brass.
We only get to control a die on the threads for the length or press it against a shell holder, and if we don't like the diameters that result when we get to any particular length, we have to select a different die. Your small base die is supposed to use a smaller set of diameters than a standard die. While you get a choice of where to screw it down, you are stuck with the diameters that are cut into a die.
Your system of trying to size brass for use in multiple chambers may or may not require a small base die depending on your luck. How deep your personal tool set runs is up to your budget. I encourage folks who are starting out to try a set of those incremental shell holders for controlling the position of the dies. This is just another good option, you don't have to do it this way. It takes less skill as a rookie to close the gap between the die and a shell holder compared to allowing a gap by backing off the die. Many ways to skin the cat and as always, YMMV.
Good Luck.