Take the following example (I'm a guitar player, so I'm going to give a guitar-centric example):
Let's say you start by playing an A major triad using the C-shape. So you're fingering the 9th fret on the G string (E), the 11th fret on the D string (C#), and the 12th fret on the A string (A). You strum it. Mountains move. Angels sing. You know, the usual.
Now let's say you're feeling a little bold and instead you play that triad by playing the A string open, without fretting it. The other fingers stay right where they are. It's not an inversion (says the novice with far too much conviction) because the A continues to be the bass note. But it's a distinct voicing change.
Is there a name for this?