Jazz pianist and author here.
When I see Dsus I’d consider D G A where G the 4th is being suspended. Dsus4 and Dsus means the same thing since sus stands for suspending the 4th nit the 2nd.
Dsus2 is a mention to play D E A. If the composer wants both supensions of the 2nd and teh 4th he’d wrote Dsus4(add2) or maybe Dsus(add2).
C/D is a slash chord that dictate how to play a D7sus or D7sus4 chord, C major chord includes the b7, 9 and 11 (C, E, G) or any of its inversions.
So C/D can’t be written as Dsus. I’m sorry to say that you’ve laerned the wrong lesson or from a wrong person.
Be carefull how sus is used either alone or 7sus, 9sus, 13sus, 7susb9, 7sus4, -7sus, -9sus, -13sus etc… there should be usually a mention what to be suspended. So, sus only means sus4 where a major triad has the fourth instead of the third.