relationship between battery voltage and discharge rate
is a 4V battery able to discharge at a higher rate (C rate) than a 2V battery?


Maybe. Voltage represents the extent to which electric charge wants to flow from the "+" side of the battery to the "-" side. So, a battery with a higher voltage exerts more force on the electric charge, which might result in the charge moving faster, depending on how whatever is connected between the battery terminals responds to more force. Many circuits will permit charge to flow faster if the voltage is increased, but some will hold the rate of charge (current) constant, while some may even respond to a higher voltage by permitting less current.

But, how fast the charge actually flows depends on what's attached to the battery, to what extent it impedes the flow of charge, as well as the internal resistance of the battery.

Furthermore, if we are talking about the "C rate", we are talking about rate of discharge relative to the capacity of the battery to store electrical energy. So, a low capacity battery will have a higher rate of discharge relative to a higher capacity battery, all else being equal, because the discharging is a larger fraction of its capacity.

If your goal is to discharge a battery as quickly as possible, then you would want to do all of these things:


connect the terminals with a low impedance, like a really short, fat wire.
use a battery chemistry with a low internal resistance
use a high voltage battery
use a low capacity battery