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Promising and actually doing it are two different things.
Literal
Promise-do-[nom-の][and-と] carry-out-[nom-の][and-と] [topic-は] different thing [copula-だ].
The pattern [A するの]と[B するの]とは違うことだ — an elegant structural contrast using の as a nominalizer twice, joined by と, and marked as topic. 実行する ('put into practice, execute') pairs naturally with 約束する as the 'promise/execute' dichotomy. 別のこと ('a different thing') makes the separation explicit.