Does Immortality grant actual immortality?

There are two capstone abilities that grant “cures for aging”

The wizard has the immortality arcane discovery:

Benefit: You discover a cure for aging, and from this point forward you take no penalty to your physical ability scores from advanced age. If you are already taking such penalties, they are removed at this time. This is an extraordinary ability.

The Alchemist has Eternal Youth grand discovery:

Benefit: The alchemist has discovered a cure for aging, and from this point forward he takes no penalty to his physical ability scores from advanced age. If the alchemist is already taking such penalties, they are removed at this time.

But these do not specifically state that the character will stop aging.

The age resistance spell specifically states that it does not stop dying from old age.

You ignore the physical detriments of being middle-aged. This spell does not cause you to look younger, nor does it prevent you from dying of old age,

Whereas the longevity mythic ability specifically states it does.

Longevity (Su): Upon taking this ability, you can no longer die from old age. If you have penalties to your physical ability scores due to aging, you no longer take those penalties. You still continue to age, and you gain all the benefits to your mental ability scores.

So does immortality/eternal youth stop aging, or just the stat penalties of aging?