Don't worry about it! First time I had to try and understand this stuff and the lecturer said, "Now we are going to have to get an understanding of imaginary numbers" I was a bit stumped.
For us, for all practical purposes ESR and IR are interchangeable. AFAIK IR is the correct usage for batteries.
Just think of a battery as a container that includes a voltage source (that varies with state of charge) in series with a resistance (the IR of the battery). The more current you draw from the battery the lower the terminal voltage and the hotter it gets because of the power dissipated in the internal resistance.
Originally Posted by Aviefly
Wow thanks John. I think I got something wrong in my question as that isn't likely to be easy for most. I think I got the idea of it, thanks for taking the time.