I suspect that you are making it more confusing then it needs to be. How about this: Any circuit being powered requires two connections to operate, a 2 wire voltage source. There is no need, and sometimes required, that neither wire to be 'grounded', which then is named an "isolated voltage".
There are situations where one must ground one of the two power supply terminals, but that is determined by the circuit under test and whatever else might be wired to it. Best supplies offer a choice of isolated or ground referenced voltage, and having the option is always better off. Recall that battery powered devices require no ground connection to operate, as a battery is an example of a isolated voltage source.