ELI5 the difference between "design-based" and "sampling-based" research (+ other variants)

I see econometricians use these terms often. There's a new Borusyak and Hull short working paper that shows that "design-based specifications"---as opposed to potential outcomes models---are not susceptible to the negative weights problem highlighted in recent work.

This Athey and Imbens working paper states that in a design-based perspective, "the stochastic nature and properties of the estimators arises from the stochastic nature of the assignment of the treatments" as opposed to a "sampling-based perspective where the uncertainty arises from the random sampling of units from a large population."

And apparently design-based perspectives are more common in RCTs?

My questions:

  1. Does anyone have a simple way to distinguish between design-based vs. sampling-based perspectives?
  2. What is the relationship between the explanation by BH and that by AI? Small point of confusion: BH contrast "design-based" with "potential outcomes", whereas AI contrast "design-based" with "sampling-based". What is the relationship between potential outcomes and sampling based?
  3. Are there other perspectives?
  4. What does the distinction mean for an applied microeconomist? When one is studying a natural experiment using administrative data, which perspective does that fall under, or is it rather that different econometric techniques correspond with these different perspectives?

Thanks!