Are all amp hrs equal?

To add to your confusion on lead acid battery "Capacity", you also have to remember that temperature, and the Peukert effect are only applicable if the current conditions remain the same, ie temperature or discharge rate. If you warm up a battery that has only been able to deliver a small amount of current, it's ability to deliver more current at a higher voltage will rise. Peukert effect only applies if you maintain the current discharge rate. If you discharge a small battery bank at a high current rate for say running a microwave off an inverter, you will quickly encounter a low voltage cutoff on your inverter after having only pulled a few amp hours. The battery voltage will quickly recover however after you remove the load, and if you then apply a load at say the 20 hour rate, you will still get close to the same amp hour total when you add the amp hours you pulled at the lower rate to the amp hours pulled at the high discharge rate.