In أَدَّبْتُهُ تَأْدِيبًا the verbal noun shares a root with the verb and can be parsed as a cognate/absolute object.
In ضَرَبْتُهُ تَأْدِيبًا it gives the reason for striking.
The same written ending does not establish the same syntactic role.
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Absolute Object versus Reason Complement
Al-Mafʿūl Lahu: Expressing the Reason for an Action
In أَدَّبْتُهُ تَأْدِيبًا the verbal noun shares a root with the verb and can be parsed as a cognate/absolute object.
In ضَرَبْتُهُ تَأْدِيبًا it gives the reason for striking.
The same written ending does not establish the same syntactic role.