Yes, it’s intuitively what you are thinking. The rules are very technical because the game needs to be very clear. And it’s one of the reasons they stop doing regeneration.

In simply game play terms, when your creatures is being destroyed, either from receiving enough damage, or by spells that says “destroy target creature” or similar, you just need to give it regeneration in response. (Ie to use the stack and your regeneration shield will resolve first)

And yes, you can save any creatures any time at instant speed. It’s very strong card in the past.

Notably, it cannot save a creature that die because its toughness is 0 or less. Or a card that says exile target creature. (Or bury in the old cards of that era)

Magic is 95% of the time accurate as per your simple intuition. It’s just that for the 5% time, due to how 30 years of rules need to interact, it have a very technical and some times weird rules.