To me, the character is the same, but the body is different.
The way I see it, the Borg Queen is a mind that exists spread throughout the Collective, just the same way that a person's mind is spread throughout all of their brain cells. The Queen that we see isn't really the Queen, it's really just a puppet controlled by the Queen's mind. So when the Queen died, only the puppet was destroyed, but the mind behind it was just fine. Just needed to get a new puppet.