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.
Best Answer
An article from Toms Hardware does a very good job at explaining RAM timings
Source
I would go with the tighter timings they tend to be faster and the 166mhz difference will not even be noticeable. In fact they are both so close that you would not notice any difference in speed. The one with the higher Mhz rating might be best for over clocking since it will give you a little head room since modern Intel and all AMD chips have integrated Memory controllers so as you up the FSB the you will also be over clocking the RAM. But again this is all personal preference depending on what you will do with your system. Either one will be fine if you are just building a stock system that you don't plan on overclocking.