Sometimes a short question requires a long, multiparter answer.
Addendum: I just remembered TGM, which is used by the GM Trainer and GM Cannes. The T here stands for Trainer and the rest is your preferred version of GM.
The website I mentioned: https://www.angelfire.com/zine/trd/etc/Gundam_Project_Mobile_Suit_Model_Numbers.htm
Zeong Development History: https://www.youtube.com/watch?v=Kv9f4I1htC0

I think RMS is the designation for mobile suits created by Zeonic engineers for the federation. They took the MS zeon suits have, and added an R to it.

7:47 Robot Armored Suit, RAS. Gundam and Macross regulary exchanged materials in backroom deals, it is basically the Queadluun Rau / Zentradi/Meltrandi Power Armor.

I have a theory for why the Titans era Federation machines used RMS instead of RGM. Zeon units used the MS designation and since many Titans mobile suits had very Zeon esque designs it's not a big leap to assume that they were adapted from unused Zeon mobile suit plans. Maybe at one point they were meant to be Zeon suits but after they lost the war the designs went to the Federation who simply added the R in front of the existing model number of those suits and just rolled with that naming convention for a while.

11:33 I love it when cities in my state are in anime such as Augusta Georgia/South Carolina.

See, I always assumed the R in RX-78 stood for “Ray”, since Tem Ray was a head engineer for project V, and the R just kinda stuck ever since

I guessed the "FD" for the Gustav Karl was "Federation Designed" because it was one of their first mobile suits developed in house under the Federation as opposed to Anaheim.

One theory for the number being a year off is they may use fiscal year, not calendar year. In the Air Force, out aircraft tail number had the year it was contracted. Tail 93-1563 was contracted (the contract for purchase) in 1993. But the Department or Defense uses the fiscal year, so it could have been signed from October 1992 to October 1993.

The RGC-80 contract could have been signed just after the 0080 fiscal year started in the Federation, making it a 0080 model year.

Just a guess though.

I remember reading a long time ago that the reason the Rick-Dias has two model numbers is because Anaheim wanted to conceal the fact that they were developing mobile suits for the AEUG; Internally, it was designated MSA-099, but officially it was designated RMS-099 so as not to draw any unnecessary attention from the Titans.

RMS mobile suits are those developed by Zeonic after being absorbed by Anaheim Electronics.

RMS is a combination of Federal and Zeon nomenclature, with the R coming from the RX and RGM lines and the MS coming from Zeon's naming convention.

The D in D-50C Loto might mean Downsized
since the HGUC Loto manual chose to use ダウンサイジング(downsizing) in its description over other simpler Japanese words.

This feels like that feeling i had with math having letters

I think there's the possibility that "GM" is intended as a build on the term "G.I." from military usage, basically "Government Issue."  GM would mean something like "Government Issue Mobile Suit." Or "Goverment Model" could also work.

Another difference is that a lot of the “RMS” units seemed more specialized/experimental than the RGMs. Which is why things like the Loto or the Gustav Karl aren’t part of it. A lot of Char’s Neo Zeon MSs are made by Anaheim, so it’s possible the “A” is for “Anaheim”

5:39 The Gate of Zedan was a way more badass name than A Baoa Qu

RAS-96 likely refers to Refined AShimar 0096, same designation phenotype as the RGZ family.

Unicorn Gundam during the series development probably was nicknamed Anaheim Electronic's Unicorn Gundam (AEUG). Gundam Unicorn (Gundam UC) is pretty much a pseudo Zeta Gundam reboot. With Full Frontal replacing Quattro.

Anyone ever notice around the Zeta period, a lot of the suits shared the Zeta chest? Driesen, Bawoo, ZZ, Zeta, even the Tristan and others have that distinct chest that comes out, red hatch, and small rectangular yellow vents. Not sure if it has to do with the moveable frame, but its interesting

The FD could stand for Federal Defender. The FD-03 was heavily armoured and was used to defend critical Federation locations during Unicorn and Hathaway's Flash

Maybe the Loto gets a different model number scheme since it was manufactured by SNRI like later UC EFF suits?