The Wolverine who teams up with Wade is a different Wolverine. The Logan who died is still dead, which the opening makes extremely clear when Wade digs him up.

The Wolverine who teams up with Wade is a different Wolverine. The Logan who died is still dead, which the opening makes extremely clear when Wade digs him up. The new Logan survives repeated stabbing and shooting during their fights. By the time they finish wrecking the minivan, both of them are exhausted and unconscious. Healing lets them survive the fight; it doesn't mean they can keep going forever without stopping. They also survive disrupting the Time Ripper together after being warned that doing it would kill them. That is the outcome of the scene. We aren't given a medical explanation that lets us calculate what either one could survive alone under every other circumstance. So that's where I'd leave the comparison. Across these films, he can recover from gunshots, burns and terrible physical damage. His power can be drained, suppressed or weakened. It doesn't always restore his memories, doesn't regenerate the metal, and doesn't make every version of him immortal. The actual examples are interesting enough without turning every survival into proof that nothing can ever kill him.