We need to bring “ignorable treatment assignment” back it into our vocabulary

Unconfoundedness, conditional independence, and ignorable treatment assignment

What’s the difference between unconfoundedness and ignorability? Mathematically, best I can tell, nothing. The phrase conditional independence, which I think Angrist and Pischke used more often or maybe first, is more or less synonyms for both. They all have the same notation:

(y0,y1) _||_ D | X