But that isn't a moral difference, that's just explaining what the status quo is.
It doesn't seek to say why it may be right or wrong to remove someone's right to life, nor explain why society deems it acceptable to remove someone's liberty for their entire life with no hope of redemption or parole yet stop short of just killing them.
God my response was slightly pompous! I don't think this will be any better sadly!
There is a moral difference between the state killing or not killing prisoners. When the government dishes out fatal vengeance or retribution disguised as justice, it becomes complicit with the killers in devaluing human life and human dignity. We can not, in my view, say killing is wrong and then kill the killer! To kill (generally) goes against our nebulous and fluid moral code
In this country our moral code is encapsulated in our Constitution ( based on statute, common law/ laws established through court judgments, parliamentary conventions and works of authority ) in the customs and practices associated with the application of that Constitution, in public opinion and in the complex underlying moral code on which society is built. This sets the very wide ( and quite fluid) boundaries of what we consider acceptable. As this is not entirely codified it is, of course, open to interpretation and change. I suspect that with the rise of populist politicians it is likely these boundaries will change again but at present we as a society are not minded to accept judicial killing via the death penalty. We consider that wrong. We are prepared to accept imprisonment without chance of parole and consider that a fair response to a terrible crime. Why we do that is tied up in that complex web of Constitution, custom and practice that makes up the unwritten morale code on which our society is structured. That code, in itself, is based on the Judeo-Christian history of western society with all the contradiction that brings! Essentially, the bible told us killing was wrong therefore society generally considers killing wrong.
Personally I feel the death penalty constitutes an "cruel and unusual punishment" ( to steal from the yanks!) that is at odds with our wider "western" moral & ethical code. It potentially fosters a culture of violence, and teaches people that the way to settle scores is through violence, even to the point of taking a human life. It also seems we treat the death penalty in a unique way. Crimes other than murder do not receive a punishment that mimics the crime - for example rapists are not punished by sexual assault,people guilty of assault are not ceremonially beaten up. Arsonists do not have their homes burnt down. My view is that life imprisonment without possibility of parole causes much more suffering to the offender than a painless death after a short period of imprisonment.
BTW - I entirely see the other side of the argument: that the defendant ( generally) is a free moral actor able to control his own destiny for good or for ill, who chose his own path, that he is not an animal with no moral sense nor as someone who ( generally) does not know right from wrong, that some crimes are so awful as to completely breach our moral code and that they are often undertaken by people who are a constant menace to society and cannot abide by that moral code and so must be punished harshly. I can also see an argument that capital punishment restores the dignity of the humans whose lives were ended by the defendant's actions