Hypnotherapy has the advantage of being able to communicate with the subconscious in a two-way fashion. Affirmations don’t facilitate direct responses from the subconscious; they only seek to speak to the subconscious.
A post-hypnotic suggestion is also different than an affirmation: effects tend to be more direct, more specific, and more immediate when using post-hypnotic suggestions.
Other than that, the language of hypnosis and of affirmations is similar. Both are always expressed in the present tense, and always in the positive. If you ever meet a hypnotherapist that uses the words, “don’t smoke” as a direct suggestion, choose a different hypnotherapist!