"Persuasion" implies that you make people share your point of view through the use of your rhetorical skills without necessarily entailing scheming or deceit. "Manipulation," on the other hand, involves a certain degree of deception to promote the interests of the manipulator. This element of deception must obviously remain hidden for the manipulatory process to be successful, the manipulator should know the emotional and psychological weaknesses of the victim and have no scruples in using them to his advantage. Of course the manipulator does not necessarily need to be an individual, but can be an institution. Totalitarian states use propaganda to manipulating effects, while the media are often accused of manipulating public opinion.
Persuasion and manipulation are related indirectly as both are part of human nature. There is difference between both the terms as one is related with the agreement of a party while in other the person is forced to do something illegal or that won't benefit him.
To manipulate someone means to force him or make him in doing something while hiding the side effects or problems that can occur in doing that work. Manipulation creates negativity and loss of trust.
Persuasion means to persuade or convince someone in doing something with providing reasons, by influencing him and showing him and giving him the full view of the work. Persuasion creates trust.