Before you read all this - I don't think you need to worry a lick about it at all. Bookmark this thread for a year from now once you've reloaded and shot all the cases you have a few times. Walk before you run. Sort your brass into same headstamps, pick the one you have the most of, and start cranking out basic handloads with basic tools to convince yourself you can do it without blowing your self up
Don't sweat details like this until you've put a few hundred handloads through your rifle. You're going to have enough headaches with more basic steps that are more important. First step is make your handloads shoot better than the factory ammo doing nothing but changing powder weights. You'll get there in your first two or three batches.
You pretty much nailed it by saying powder capacity.
To build off of what Mike said ^^^, using water to measure the actual VOLUME of each case is the critical measurement that the task is trying to get. If the internal volume is the same, then the same mass of powder poushing on the same weight of bullet sat at the same point in the neck should result in very similar pressure curves on each shot.
High level answer - consistent pressure curve = consistent velocity cuve = consistent ballistics once the bullet exits the barrel.
The red line is chamber pressure, and it has to stay below a certain maximum to be safe. The max varies based on a lot of variables, but cartridges that are approved by SAAMI and used by the major manufacturers all stick to the maximum spec for ammo. If the red line goes high enough.. rifle blows up.
The blue line is velocity, and it what results from the expanding gas of burning powder acting on the bullet. There's a ton of things to go into defining that curve (length of bullet bearing surface, bullet metal type, coatings, throat design on the chamber, etc.), but the goal is to make it very consistent. All brass prep and bullet seating and powder charging and every loading step goes towards making the red and blue lines as close to the same each shot as you can get.
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Now about the two processes to accomplish this:
A lot of guys use case weight to approximate case volume because it's a much easier process than volume sorting. Put the case on the scale and record weight, easy. When I do this I write the weight on the side of the case with a Sharpie and if I drop my tray I don't have to redo all the work. Sharpie wipes off easy when I'm done sorting.
Case weight sorting can be helpful if you know that cases come from distinct sources and it's a fast way to separate them out. Like if I have three boxes of factory ammo with the same headstamp and the cases got mixed up, I should be able to weight sort back into three groups to match the boxes they came from. More than good enough if you're starting with once-fired factory loaded brass.
But there are several things that can make the two measurements not correlate - the extractor groove cut is the primary one. The case head where that cut is made is the heaviest, most solid part of the case, so two cases with the same external weight can have the different internal capacity, and vice versa, based on the wear of a tool during one of the least critical steps of case manufacturing.
So to chase the best precision possible - inside a group of matched cases (ie 100 Lapua cases from the same box), weight should be very similar because they were all cut at the same time. So taking the next step and measuring actual case capacities using liquid to create sub-groups from that lot is required because weight sorting won't really tell you much on high quality cases. Vince mentioned minor details is case manufacturing and several reloading steps that can also affect volume, it's not just one thing that can do it.
I only do water capacity sorting on the most demanding things I load for - mainly 1000 yard benchrest and ELR, but also 17 and 20 cal cases and wildcats that I have to form brass for. On most hunting rifles (even long range ones) I can normally get good enough precision from the rifle without taking that step. But if you're shooting a load and a known good rifle is being weird then it's a good process to be comfortable with to rule out a potential issue.
