First, let us take a look at the meaning of Persuasion – The action or process of persuading someone or being persuaded to do or believe something (synonym includes coercion, inducement, urging etc).
You could easily find that the internet is filled with websites that have very long sales copy writing that is deliberately designed to persuade people to buy their products. They use persuasive words like “limited stock last”, “discount for now only”, and paint rosy images if you were to own them and make you feel bad if you miss them now.
Yes, in a way, hypnosis is a form of persuasion. However, it is only one of the many aspects. You have to look at the context to determine it. For instance, when used in a therapy setting, it is not persuasion but positive suggestions.