I don't think there is a usual definition. I have seen varying definitions of immortality. The immortals in Highlander could only be killed by beheading. The immortals in Gulliver's travel couldn't die at all, but continued to age, resulting in an island full of senile people.

I think the two most common definitions I have seen are "negligible senescence" (e.g. Elves in Tolkien) and "cannot die in any way" (e.g. some religion's understanding on the concept of an immortal soul). The latter is fairly common and matches "cannot ever die even if you want to."

That's the form of immortality in the story.