Manipulation serves the manipulator's interests, not the interests of the person being manipulated. Manipulation appeals to the emotions of the person being manipulated (If you really loved me, you would.... ) There is usually a penalty of some kind involved if the person does not acquiesce to the manipulation, and a reward (or a promise of a reward) if they do.
Convincing serves the the interests of the one being convinced, not the interests of the person doing the convincing. Convincing relies on presenting a complete body of factual evidence, rather than appealing to emotion, and allowing the person to make an informed decision. The reward/penalty aspect doesn't enter the equation.