It's actually the motor controller that determines what voltage is allowable and how much current to deliver. The motor can run at high/low voltages. With a commercial ebike, one should stay with the manufacturer's battery spec for voltage, but you can always go with higher AH, as that just means the battery has more capacity to increase your range.
In the DIY world, hobbyists can select the controller power and not have to match it to the motor, at their own risk of course. SInce I have both 36V and 48V batteries, I like my controllers to be able to run on either. I also lean toward higher current controllers because it's better to have more power and refrain from using it than to not have enough.
Batteries aren't really rated by watts. They're rated by AH. They will tell you the voltage and AH and often leave out the continuous/max current. The AH and continuous current are related, but don't have to be. Some cheaper batteries could have both a highAH rating, but not be capable of supplying high currents. WIth a commercial ebike, you just buy what they recommend as a replacement. WIth a home built bike, you have to make sure the battery can supply the max currents demanded by your controller choice.