What are the AC characteristics of a battery?
The "AC characteristics" have to do with how the battery responds to rapid changes in load current or charging current. 

The simple fact is that a battery is NOT "just" as voltage source and a series resistor. The electro-chemical reactions inside the battery take time. Thus, you can apply a sudden charging current and the terminal voltage will take some time to settle to the steady voltage it will have.

This is particularly important when you use a PWM charging current (that is, pulsed, with a varying on-time). In this case, the AC characteristics are particularly important.

I do not know how these characteristics differ between, say, lead-acid and NiMH or LiIon.