Overthrowing it with treason implies:
-betrayal of the traitors' oaths. Also, you betray the trust of the people who put you in office (the country)
-violence -> you opened the gates and the barbarians sacked the city
-loss of independence through force. the people are no longer represented at all because the ruling government is a different one (say, beijing)
-etc.
Changing the government through votes means that unless all the votes that overthrew the government were forged, which doesn't happen, a popular opinion is still represented.
So if you had a referendum, and the outcome was 51 to 49, even if 2/51 was forged, you still had a pretty large group of people who wanted to vote one way or the other. And it doesn't imply violence. And unless the forgery was done by the government itself, there is no betrayal of trust, no betrayal of oath and public duty.
So yeah. There is a big difference. Sure, the outcome is the same, but the means and the implications vary greatly.
Overall, the death sentence is a barbaric method. It is also unchristian if you happen to be a devout Christian, you shouldn't support it for any crime except treason. Because treason supercedes religion. It goes against nature. Evolution itself despises treason and that's why you don't see treason in the animal kingdom. So a traitor can no longer be considered human. Just a monster.