MDG – Yes, your interpretation would seem correct based on the Gemara. However, look in the Rambam (Rotzeah, 2.2-3) who says that there is no “death at the hand of the court” for the crime of suicide, only “death by the hands of Heaven,”. This is puzzling, since how could a suicide, no longer alive, be punished for the crime by the court?
It would probably be better to decide that we don’t understand what these terms mean.
Goldilocks – I would suggest that the actual punishment might depend on whether the individual (while he was still alive) would prefer punishment in this world or the next. If so, then there is a fourth type of Kares – the type where the individual does Tshuva M’Ahava and is rewarded in the next world. We’re all capable of being Maccabees!