The motors will run in general on any voltage, but your controller may not be able to run on higher or lower voltage, Some of this may be component voltage ratings. Some of it may be hard wired voltage references inside the circuits.
Some controllers are dual voltage. They determine whether it is 48V or 36V when the battery is connected, and set the correct low voltage cutoff. Most of my ebikes use dual voltage controllers. I like the flexibility to use either type of battery.
One honest thing about e-bike batteries is that they determine the amp-hour rating by adding the up the individual Ah ratings of the cells in each group, A 48V pack made up of 52 cells with 4 cells in each group (13x4) will be a 48V13Ah pack if each cell were 3.25Ah. A 36V pack made with 40 of the same cells and also 4 cells per group (10x4) will be a 36V13AH pack. Although both of these are 13Ah, packs, they are not the same, as you have to multiply that by the voltage to get the nominal watt-hour, which is 13x48 and 13x36. Clearly, there is more watt-hour capacity in a 48V pack, and that is one reason I like them.
I can also go faster with 48V, but that's not a big deal to me, since I go fast enough on 36V. Some of the performance brands sell bikes with 52V batteries (14 series groups). Most controllers that can take 48V will also take 52V. Mine will, and while I have a 52V pack, I don't need that kind of speed. I bought it just for bragging, Kind of wasted the money since I don't need it,