why does a dead button battery still put out full voltage?

[AutoDoc Williams]

My inexpensive multimeter has a '9v battery' and '1.5v battery' test position. I believe they put an appropriate resistance in series with the battery to determine whether or not it can deliver the power it is designed to.
Am I thinking along the right lines, please?

Yes

 

[Spectric]

No one has yet come up with why the battery voltage drops under load, a clue is that you have cranking batteries and deep cycle batteries, aka leisure battery.

The cranking battery provides high current over a short duration as given by it's cca rating and a leisure battery provides a steady current over a longer duration. It again comes down to ohms law and the answer is the batteries internal resistance, it has to be low in order to deliver the cranking current but at the expense of capacity.