The bodies are cloned, but they're the original person. At least with Ben Reilly (Amazing Spider-Man (2015) - #22), he was brought back every time he died. The Jackal brought back the Lizard's wife and son, and in issue 21 of the current Spider-Man run, Doctor Strange said that (at least for the son), they're the original person. The implication is that cloning can legitimately bring someone back from the dead.
The writing in the X-Men books treats them like the real deal, too. You're basically just reloading a save state.