Adding a little more detail to what John said, battery boxes can provide different voltages and frequency responses. For example, the series resistors in our HEB battery box is different than the one for our Low Cost Binaurals, despite them both providing nominally the same voltage. Too low a resistor value and the HEB's DPA capsule is in dangerous territory.
And the battery box for our CS Binaurals is a drastically different voltage than the HEBs. The voltage is selected to optimize performance.
So to answer the original poster's question, battery boxes can differ not only by brand but also by model within a brand's product line.