How to choose Vdd and Vdds supplies ? When and why should they be different?

I should have mentioned that in this case LTC6820 interfaces over isoSPI with DC2259A  (LTC6811-1 demo) . I don't know if this interface requires +5V on LTC6820 Vdd pin or any voltage within the range specified in the datasheet would be OK.

Bird said:

But what could be a reason to make Vdd (powering the chip) any different if 3.3V fits within the Vdd range of the chip? In other words what could be a case ever making Vdd any different from Vdds and always match the MCU voltage whatever it is in reference to MCU ground?

There aren't many reasons to do this unless it's convenient to the system already (i.e. a 5V rail capable of sourcing the VDD current already exists while the 3.3V low voltage for MCU serial has heavy current limit).  There is a difference in the isoSPI common-mode range which can provide slightly better EMC performance, but the impact is quite small.

Bird said:

If I connect the DC2792B with my MCU board (which is powered with 3.3V ) , can I power DC2792B both Vdds and Vdd with +3.3V instead of shown +5V?

Yes, this is the intended way to power LTC6820 or ADBMS6821/ADBMS6822

Note that ADBMS6821/ADBMS6822 are also available now and perform the same function as LTC6820 but in a QFN package with higher pulse driver current and better common-mode receiving range.  LTC6820 still works fine even with the newest ADBMS6830B and ADBMS2950B parts, but depending on the project, particularly if it will be produced in volume we'd recommend using the newer ADBMS6821/22.