Saving Throws: A Summary

That it's a "saving throw" and not "saving roll" as in "attack roll" or "roll your THAC0". Language weirds.

Some games lack saving throws; instead, the character is expected to explain or act out how exactly their character avoids the whatever. A game master can judge how well their plan would work, or the other players can vote, with the game master as a tie-breaker. In this case roleplaying is being selected over efficiency of combat and probably also realism.

Armor class can be considered a saving throw against incoming damage. Other special attacks often totally bypass armor, in which case there are often specific saves against those specific attacks, especially for "better" or "higher level" units with more experience or Heroism about them. Specific saves might become general categories as a game complexifies: a wargame might have "save against catapult" that turns into "dodge fireball" or "save vs. dragon breath" or similar.

Wargames in the 1950s had saving throws, or possibly even earlier games. Does your unit get wiped out, or not? Or does the crew suffer a morale failure, or not?

"fireball" from wizard was similar to "large catapult" in wargame, similar rules for saving used

regular / hero / superhero distinction from wargames probably turned into level-based save

There were some early complications where Dungeons & Dragons had different saving throws for wands versus staves; wands, rods, staves in later editions got lumped into one category. Other complications were "if a wizard makes a magical trap, what saving throw is involved?" Dragon breath to avoid the area of effect? Or is it like a spell-in-thingy like a wand roll? Or save vs. spell as if cast directly by the Wizard? Other? There may be house rules here.

Realism need not apply, like hit points saves are an abstraction. Also if there's a fire-breathing dragon, how is realism involved…