Both tadhyīl and takmīl improve an utterance, but in different ways. For tadhyīl ask: how does the added clause confirm the earlier assertion? For takmīl ask: which unintended interpretation would have been possible, and how does the additional wording exclude it?
DevicePrimary functionTypical form
TadhyīlReinforces an earlier meaningAn additional complete clause
Takmīl / iḥtirāsPrevents a contrary inferenceA qualifying expression that blocks misreading
An expression may have several benefits, but the primary rhetorical function guides classification.