You own your own keys, though there are caveats to that statement apparently.
Custodial lightning you don't own them.
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but user privacy is equivalent to custodial lightning, correct ? the ark custodian sees all ?
Custodial wallet means you don't own your own keys.
It's correct to point out that this implies bad privacy too, but that's not the definition of custodial. And the implication does not apply in the other direction.