The second part of your post looks almost textbook. A battery can be viewed as a voltage source in series with a resistor. Hence comes the term equivalent series resistance (esr).
As JonSea noted, that usually doesn't make a difference. However, in your two examples, the resistance of the battery is halved from about 9 ohm to 4.5 ohm. Using your equation, the calculated R is 17 ohm. That would be the total resistance of the series circuit. So, the 1-A battery would need a smaller series resistor than the 2-A battery for the required current.