Immortality

What is the difference between the powers invincibility, invulnerability, and immortality?

Can someone who is immortal use their immortality in some way to heal someone else? Like in a sense, transfer some of it to them to heal them.

Like person A has a burn scar they want healed. Person B is immortal. Could they transfer some of that immortality to someone else to heal said burn scar?

I'm making a story where some people in the world have varying immortality ranging from semi-immortality to the main three characters who have absolute immortality. There is a business/company that hires only immortal people with regenerative healing factors and above but I'm having trouble figuring out what the company does and what the jobs would be.

So what do you guys think this company and varying jobs should be?