Nottingham City Transports fleet all has electric destinations with the vast majority being Mobitec (either in orange or white) and some using white Hanover displays (as well as maybe a third type being trialled?). All of these buses have a separate destination display controller to the audio-visual system - they aren’t linked. So drivers have to ‘manually’ press a few buttons to set the right destination each time.
The Audio visual system is supplied by ‘init’, who also provide their ticket machines (which look more like a tablet fixed onto a stand with a separate printer module) and card/pass/QR readers. This system also provides the GPS tracking and maybe even the radio these days. This system knows which running board it’s bus is allocated to and so the ticket machine automatically updates the Audio visual at the start/end of each journey.
So in short, these systems aren’t at all linked so I can’t imagine the same software is used for both.
Whilst this only applies to NCT for certain, I imagine it is the same/similar for most UK operators.
In Europe, I believe it’s common for the destination displays to be controlled by the same thing that controls audio visual - an ‘ibis’. But then these sometimes aren’t linked to the ticket machines themselves.
There probably are operators around somewhere in the world which have a ticket machine, destination control and the audio visual control all in one - likely ones where they changed/upgraded all systems in a similar time period.