The word immortal comes up all over the place, and is used in many different ways, even if you were to say that for something to be immortal it can't ever be killed, there are numerous ways to do that.

Basically I break it down into three groups:
The Invulnerable, meaning they can't be hurt whatsoever, usually there's some odd exception just for effect, like the guy with a painting of himself that ages and is injured in his place but if he sees the painting it all comes back to him; It's simply impossible to cause meaningful damage to them.

The Unkillable, meaning you can cause as much harm to them as you please, and their body will break, but they will heal from any extent of harm. For example in the TV series Dead Like Me the main characters are all Grim Reapers, and already dead, so regardless of the amount of injury they incur, such as a piece of rebar through the heart, cocaine overdose, or decapitation, they will recover fairly quickly.

The Ageless, These guys barely count as immortal, basically they won't ever just die, age or illness have no hold on them, but if you shoot one in the head it's game over

These three groups contain most if not all forms of immortality, aside from anything involving possession or reincarnation, but there's still a lot of important details, and mixing. Say for instance, maybe you've got someone who like an unkillable will recover from almost any injury, but not any injury, perhaps if decapitated, or like a vampire staked through the heart/decapitated-cremated-tossed-in-a-river/however-you-like, but if you just cut their arm off they can slap it back on. And of course if there's any healing to be done, how fast does it happen?