I've asked this of many of my friends as a point of curiosity. I have very specific definitions for both.
Invincibility is the condition that you will never die except by old age. If this is too ambiguous, then you may die at exactly 120 years of age. Your body will never suffer illness or damage except when you will it to, as in exercising. You will feel pain normally, except when you wish not to.
Immortality gives you a timeless body, one that stops aging at your physical peak (typically 25-40). Physical damage, lethal illness, starvation, and other causes of death still affect you normally, but you will never die of old age.
So which is it? What would you do with your ability? Remember, neither trait keeps you above the law, and you may find yourself in prison for life, or forever, depending on your choice.