There are many inter-related things that dictate the "voltage" of the system. One of the hardest things for people to let go of is the notion that the batteries these things use don't behave like the disposable sort you might put in a flashlight. If a motor/controller system is put together for 36V, it expects the same-sized power source. It's not like a 3V DC motorized toy that just slows down/produces less torque until the batteries die.
The electronics that are actually running the whole affair are powered at TTL levels (like the lion's share of the computer you're reading this via) - FIVE volts. What is being controlled, though - the flow from your batteries to your wheel - is set up specifically for the source and intended target. A 36V controller expects a 36V battery bank, and it also expects to be able to monitor a power source with an expected range in order to reliably cut the operation of the main motor drive when battery depletion to a certain level is detected (to save you from killing your batteries, which is a whole other thing). Your 36V wheel would not even START to spin with a 24V power source and controller attached, even though the microcontroller would be very much alive.
The way this is accomplished isn't sublte. The same controller board is used in systems from 24V through 48V, from what I've had my ands on. The manner in which the input voltage is dropped to levels appropriate for the controlling logic, and how the power is driven out (potentially) vary. The controllers may LOOK identical, but there are build differences to suit the target drive. (The way they cascade voltage regulators is an example, as well as output transistor choices).
I've done poorly at explaining this in depth, but hopefully I'm assuring you that there is a need to match your components.
Cheers!
