It depends on if you'll defining immortality according to the true concept of what it actually is. What manjaro stated in the first and second examples he/she gave is actually an example of being (1)completely immune to injury, and (2)having endless life.
To be immortal doesn't mean that you can't die by being kill(dead but body or particles of you remain) or destroyed(Annihilation, nothing remains down to the infinitesimal molecule or particle). To be truly immortal, is to have self-sustaining life, the kind of life force that is its own power source.
An immortal being doesn't need/or depend on any created thing to sustain its life essence, no special apples of power, no sun or stars, no food or water, nothing. There is nothing that sustains them or powers them except they themselves, they can breathe, talk in any environment.
People with everlasting life(perfect humans) wouldn't age, once they've reached full adulthood and don't get sick and die, but can definitely be killed just as an imperfect human would be killed, it would just take longer for them to die because of having a stronger-tougher body but still they would have human-level durability. Having immortality, means being a lot more than long-lived, whether you have a physical or spiritual body.
Most beings in comics that are long-lived and called immortal, just have a form of resistance to death/injury combined with near-endless or everlasting life that is based on the writer's understanding of
Immortality is a special gift that comes directly from God. The holy angels are not even immortal, they are spirit beings who are higher than and far more powerful than anything in the physical realm but they don't have self-sustaining life. Angels depend on God for life in the same manner as we human do, they just are higher forms of life, since they are spirit beings with spirit bodies just like God.
Jesus, was given immortality by God, after remaining faithful and accomplishing all God required of him, here on earth. A limited number of others, like his faithful apostles are spoken of in the Bible as being resurrected to heavenly life and given this special gift of self-sustaining life.