I usually hear the middle term referring to as "natural immortality," as opposed to enforced immortality which is more akin to outright invincibility. There are a couple things in our world that are naturally immortal in that they're alive, but they don't age and won't die of natural causes as it were. They can still be killed by trauma or violence, but left to their own devices they'll persist forever. These include a specific type of jellyfish, Turritopsis dohrnii, that does not age and will live theoretically forever barring violence, some species of flatworm that don't even die from trauma with their pieces able to regenerate into clones of their original form, tardigrades, and the cells of most forms of cancer.