This is not either or neither. Partly the nature of the change. Partly where and how it's played or written.
Dsus2 must be new writing and added confusion.

To save confusion of getting into advanced theory. Suspension chords usually stay on the same root. A Dsus2 chords' later chord would still be a D chord. A D9 may change to a completely different chord, like E(something). Asus9, I've never heard it called this, but it's the same thing. Like you said it's just a writing thing based on where it's going or where it came from.

Asus4, I am more readily agreeable, depending on where it is going. The assumption is that A is the bass.
The suspension is D.

Well "A" would have to be the bass note, it's not written otherwise. If the bass note was E, it would be written as
Asus4/E. Or if E was the chord it would be also named a E7sus4/A. The range of names of any given chord is almost ridiculous until you understand why they are all named differently.