Ability drain vs. ability damage immunity

[Run, Just Run]

If something has ability drain immunity does it have to have to have ability damage immunity and visa-versa, a friend says yes put I don't think this is right.

[Rocky Williams 530]

Ability damage, and ability drain are different, if not greatly so. Ability damage can be healed naturally. Ability drain is permanent and can only be restored through magic.

Therefore, I'd say if you have immunity to damage, it doesn't mean you have immunity to drain, since damage is, ultimately, less severe than drain. If you have immunity to drain, I'd say RAW it doesn't mean you have immunity to damage, though I think as GM I'd allow it, since it just makes sense to me to do so.