Yeah, there are varying types of immortality. Maybe we should define them... Tolkien's elves can die, but only through violence (and in some rare cases, sadness, as mentioned above). They are free from sickness and disease, as well.
I'd suggest calling the inability to die from old age Agelessness, though that's not quite right. They do age to some small degree.
I'd suggest calling the inability to die from old age Agelessness, though that's not quite right. They do age to some small degree.