Some are 24V instead of 12V. Some cars have more than one. Etc. That said, the normal peak current is the Cold Cranking Amps. This is the amount of current the battery should provide for starting a cold engine at 0°F. 300 to 1000 Amps is not unusual. This white paper describes a dead short test:
» Electrical » Battery Run Time Calculator The Battery Run Time Calculator is designed to help users estimate how long a battery will power a device based on its capacity, voltage, and the device's power consumption.
So, yes. Batteries have a max current drain (given by design and physical/chemical limitations) and yes the storage rating (being Ah, Wh or Joules) changes depending on battery design and load applied, and yes Wh is a better way to compare batteries because it takes voltage in account.
OCV, impedance and conductance readings were measured and each battery was “dead short” tested using the test method described above. In theory, with a perfect conductor you are looking at over 2000 Amps. With their test, they saw 1700 Amps. And these are just 33 Amp Hour batteries, small compared to most cars. These are UPS batteries!
The capacity of a battery is measured in amp hours. So, how does it work? Well, an amp hour is the measurement for how long a battery can supply a specified current for, when it isn't being recharged by an alternator. For example, a 50Ah battery can deliver a current of one amp for 50 hours or two amps for 25 hours if it's not being recharged.
Just fyi, typical drain key off (and the vehicle must sit for 30-45 minutes to ensure all modules go to sleep as well! ) is to be under 0.05 amps, or 50 milliamps. Not sure what it "should" be pulling, but anywhere near a whole amp is way too much and will drain the battery in no time. Are you sure you tested right?