The Judge's Shield (1977) predates the Dungeon Master's Screen by about two years, give or take some months. (That the Judge's Guild got to this first is not surprising, as Gygax infamously told them that nothing but rules would sell, and the Judge's Guild was fated to prove him wrong.) So the term “shield” was established before the term “screen”, and still has minority currency today.

The Referee Screen (1979) for Traveller has the same vintage as the DM's Screen and is the only other data point before the 80s begin. It's unclear which was published first that year and therefore which one coined the term “screen”, but together with their two popular games — D&D and Traveller — they certainly had a large enough combined audience to establish the term “screen” in common usage over the the term “shield”, and likely TSR's audience alone would have been enough to establish the term as definitive. (Judge's Guild material, although designed for use with D&D and acclaimed at the time, was not “official” and that would have prevented a lot of play groups that didn't stray from TSR-branded material from being exposed to the alternate term.)

The history isn't very interesting, unfortunately. The only reason we have more than one word for it is because “shield” enjoyed first-to-market advantage in establishing mindshare enough to not be completely destroyed by the TSR juggernaut's adoption and promulgation of the term “screen.”

The “GM Screen” variation, as noted in the other question's answer, is merely a variation of the term that follows the separate trend of the hobby adopting “game master” as a non-trademarked, non-D&D-specific term, whether out of a hobbyist's need for precision or a publisher' need to avoid legal trouble. The term “GM screen” therefore doesn't have much of an interesting history of its own. You can see “GM screens” in a few early items:

• The Morrow Project's Game Masters Shield and Reference Tables (1980)
• The Star Trek Gamemaster's Kit (1983) including a “Gamemaster's Screen”
• Avalon Hill publishing the RuneQuest Games Master's Screen (1989) for RQIII

MAD

Multiple Ability (score) Dependent means that a class needs high numbers in multiple different ability scores to function well. The archetypal MAD class (in my mind) is the Monk from Pathfinder.

Pathfinder Monks need:

• Strength: Pretty much all they do is melee attacks, so Str gives +to hit and +damage
• Dexterity: Since Monks can't effectively wear armor, their Dex bonus to AC is very important. Additionally, many of their skill proficiencies are Dex based and they have many class features that affect Reflex saves (Dex based).
• Wisdom: Many of the special attacks that Monks have force saves with DCs set by their Wis. They also get bonus AC from their Wis, and their number of Ki points is based off Wis.
• Constitution: Since Monks are melee, they will get hit, meaning more HP (driven by Con) is needed.

These are of course in addition to Intelligence to get more skill ranks

Right away we see that Monks need 4 (or 5) out of 6 ability scores to be high. Additionally, 3 of those are physical ability scores, and as such share magic item slots for items that enhance them (Str, Dex, and Con are enhanced by belts). Getting 1 or 2 ability scores high isn't too hard, but 4 is.

SAD

Single Ability (score) Dependent means that a class only needs a single ability score to be high to function well. Several classes fall into this category, including most pure casters, ranged fighters, and rogues (depending on archetype).

Pathfinder Wizards need:

• Intelligence: This determines the Wizards ability to cast spells, gives them bonus spells, gives +hit and +damage on some spells, increases spell save DC on others, helps them learn new spells, lets them counterspell reliably, and lets them use most of their proficient skills (including crafting).

There is pretty much nothing a Wizard will want to do that isn't benefited by Int, or that is benefited by other ability scores. They don't even need a high Con since they won't be on the front-line and probably won't be hit.

Because they only need 1 ability score to be high, Wizards can devote more resources into pumping that one score until it is as high as can be, and then direct those resources into other useful items without needing to stretch to cover lots of different scores. Additionally, getting a higher Con is easy since Con boosting items use the Belt slot, while Int boosting items use the Head slot, meaning there is no opportunity cost to increasing both.

What does this all mean?

Basically SAD classes are much easier to make and to play effectively. MAD classes need more resources to achieve similar levels of effectiveness, and may require more real-life time dedicated to finding obscure bonuses and builds to make up for their shortcomings. Additionally MAD classes can find it hard to stay relevant at higher levels as the effective tax on their upgrades takes its toll, especially in a party with SAD classes.

That doesn't mean that SAD classes are inherently better than MAD classes, or that MAD classes can't be effective or fun. Obviously it depends on what system you are playing (Pathfinder is much more punishing than DnD5e, for example), but DnD is a game, and you can have lots of fun with any class. Unless you are playing a high level, optimization heavy, all combat campaign don't feel like you need to shy away from a MAD class, although if you are new to the system it will obviously be easier to go for a SAD class.