Things aren't quite so free-form as i believe you are imagining.
There are two specifications in particular that define how Memory is catagorized, detected, and configured: JEDEC Standards, and SPD Standards.
Basically, JEDEC defines the timings, cycle-time, clock-speed, etc of all ram that is sold as "DDR3-12800" (just for example), so that all vendors agree that the settings will be the same for all their chips in that line. See the specs for DDR3 RAM here: https://en.wikipedia.org/wiki/DDR3_SDRAM#JEDEC_standard_modules
Your motherboard implements Serial Presence Detect (SPD), so it expects the RAM it finds to be configured such that they conform to one of the JEDEC profiles for that type of RAM.
That means that when your Motherboard manufacturer says that they supports "Up to DDR3-2133", that (among other things) it's SPD is capable of recognizing DDR ram of all DDR3 types with a transfer rate of less than 2133, and has the ability to load JEDEC profiles to configure to use that RAM.
So, thanks to JEDEC and SPD, the motherboard manufacturer doesn't need to tell you explictly what profiles they support.
What is a matched set?
Matched sets are guaranteed to work together at advertised speed, assuming no motherboard incompatibilities or defects. 2 sets of same speed, same brand and same model number are not guaranteed to work well together. It's better if they come from the same production batch, but that still does not equate a matched set, as from what I understand a matched set has been tested (to a degree) during the binning process.
Number of sticks
In addition to the risk of unmatched set, I believe that using many sticks increase the likeliness of encountering the "limits" of the motherboard and trigger incompatibilities with the RAM. Unfortunately I don't have evidence to back this up, but I have had the experience of sticks that all tested fine independently, but failed as a cluster.
If your question was about 2 sticks I'd probably tell you to go ahead and try it, with 8 sticks I'm much more cautious.
RMA considerations
If you run into issue, the RMA process will be much simpler with a matched set. I've had some issues with a new 6 stick matched set a few years back, and had to RMA it 3 times before getting a good one. It would have been troublesome to have 2 independently working products on hand, but failing as a set. Which one is causing problems? What is the chance of exchanging both to fix the issue?
However, you can do solve all those issues that at no cost to you during the return window, and save some money. Whatever you order, make sure to configure them to run at advertised speed, and memtest this seriously. If they work well from the get go, chances are you will be fine for their lifetime.
If a stick later fail under warranty you can RMA that particular set only and pray you get a compatible set in return. But that's only a chance, and much more in the future - so it depends how much you value those savings today.
Underclocking and testing considerations
I think you alluded running them at a slower speed than advertised if you run into issues. That may ease the load and avoid incompatibilities, but figuring out the working configuration is like overclocking - you'll have to do a whole lot of testing to find what frequencies and timings do actually work, if any, and testing 128GB each time is going to take a while. If you settle for frequency and timing that are much lower than needed, you have to consider that the money saved is being eaten away a little by the lower grade of RAM speed you are benefitting from.
TL;DR
For that many sticks and amount of RAM, my personal recommendation would be a matched set. But it's certainly not a bad decision to try it out if you're willing to risk having to go through a return process early on -- and maybe only switch to a matched set if issues do arise.
Best Answer
Considering the Corsair Vengeance 3200 modules in the 2x16 GB kit and the 128 GB kit are identical your assumption was correct.
You should verify you were not in a mixed memory channel configuration. In reality outside of benchmarks, you will see little improvement between small frequencies differences.
You are welcome to do that, but there isn't a performance difference, considering the physical modules are identical. The only difference would be the serial numbers would be incremental with one another.
The only differences are indeed packaging, manufacturing batch, and price. It is basically the difference between the huge bag of potato chips, or the combo pack of potato chips, which contains two smaller bags.
The compatibility list is simply the list of modules that were tested. It should be used as a guideline to find modules that are compatible (compatible frequency for example). DDR4 is a standard, so a module running at a certain frequency and timing is going to perform nearly identical to another similar DDR4 module. Other properties of the module that are not part of the standard (what type of heatsink it might have) are the only major differences between modules produced from difference companies.