My understanding is that the death penalty process is kind of a hack job and can't be done properly because no medical personnel will participate in it due to the Hippocratic oath. This is not a concern in consensual euthanasia.
There's also an issue with the death penalty process seemingly requiring suffering, as evidenced by the lack of use of inert gas which appears to be painless considering accidents with poorly-ventilated spaces where people unknowingly pass out (and sadly those who go help them suffer the same fate). Even in states where the "gas chamber" is a thing, cyanide is used instead of just inert gas despite it making the post-execution cleanup process safer (so would make sense even if you did not care one bit about the suffering of the condemned).
Even if the death penalty was perfectly humane, there are so many other considerations that this comparison is clearly in bad faith. The GP doesn't understand why the state murdering people is a different consideration entirely from doctor assisted suicide?
Absolutely, I'm not defending the death penalty in any way. But even if you do support it, my response tries to bring up how bad and intentionally cruel the current implementation is.
The OP wants to know why the same process using the same drugs is described as full of suffering in terms of symptoms for criminals, but blissful when used for assisted suicide.
(And I'm not in favour of the state killing criminals or terminally ill people).
But it's not "the state killing terminally ill people". It's terminally ill and suffering people asking for help to end their lives and their suffering.
The situation is completely unlike the death penalty, where it's about punishment.