Having Might is not the same as immortality. While it grants immunity to aging and warping, it only provides resistance against deprivation (can't recover any spent Might) and no protection against disease or trauma. (see ArM5, p.182 and TM(R), p.133)
Compare gaining might against things like "The Great Elixir" (TM(R), p.43) and other effects which grant immortality.
True Immortal vs Only Might
- Deprivation (Food/Water/Sleep/Breath): True Immortals don't suffer any penalties (except lack of speech without air) while beings with Only Might need to do all of these to recover spent Might points.
- Severe Damage: True Immortals wounds never worsens and always fully recovers in no longer than a season. Only Might wounds can worsen and do not auto recover. True Immortals also have a different Recovery roll compared to everyone else and can recover far faster.
- Lost Limbs/Organs: True Immortals will regenerate the limb after a season, while Only Might will have to use magic to regrown the limb.
- Mental Changes: True Immortals revert back any mental changes in no more than a season if they are not sustained by magic, while Only Might will not. True Immortals will always revert back to the Personality Traits they had when they gained Immortality, while those with Only Might can change their Personality Traits. True Immortals will regain memories erased by magic once the magic is no longer sustained (no longer than a season, but can be much shorter since it is a weekly recovery roll that gains +3 for every week).
- Might Stripper Spells: True Immortals specifically and clearly only take temporary Might loss by Might Stripper spells unless they are utterly destroyed (full recovery by the next day). Only Might loses permanent Might (unless you are playing with some House Rule) and reverts to mundane if all of their Might is stripped (though Might 0 is valid so enough stripper to take them into negatives is required).
- Gaining XP: True Immortals have to bind XP and new spells into an enchantment or they loss them. Only Might has a penalty to their seasonal XP equal to their Might and can offset the penalty by using Vis. Only Might also has no issues learning new spells.