Electronic – Battery discharge current

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

Standard discharge current is related with nominal/rated battery capacity (for example 2500mAh), and cycle count.

If battery is discharged with higher current - real available capacity will be smaller (it may be much smaller). Discharging battery with lower current will extend real available capacity a little bit.

Currents higher than standard will shorten battery life, lower will extend it (in comparison with nominal cycle count).

Maximum continuous discharge current is a current that will not overheat and destroy battery, but keep in mind that discharging battery with maximum allowed current will reduce battery life significantly and probably real available capacity will be less than nominal.

Here is an example, where you can see how battery capacity changes at diffrent discharge currents

Source: Panasonic LC-R121R3P VRLA battery datasheet

There is no information about maximum discharge current, however it looks like that battery can be discharged with 850mA, but you can't use whole 1.3Ah capacity.

Another example - Sanyo AAA Eneloop NiMh rechargeable battery:

Source: Sanyo AAA Eneloop NiMh HR4U-TGA NiMH battery datasheet