To persuade someone is to try to make them see your point of view. To convince someone is to succeed in making them see your point of view. That being said, people frequently use "persuaded" when they should use "convinced" (and nobody will look at you funny if you do the same). They're technically allowed to do this, as part of successful persuasion necessarily includes convincing that person, but using "convinced" in this situation is more accurate, if you can remember the distinction.

I am going to have to disagree with Grant on this one. "Persuade" is more than trying to get someone to see your point of view. If your attempt fails, you have not persuaded them, but only TRIED to persuade them. In this sense, persuade and convince mean almost the same thing. Most of the time, you can use 'persuade' and 'convince' interchangeably. However, 'persuading' requires conscious, voluntary actions, with the goal of changing a person's mind about something. This could also qualify as 'convincing.' However, things that are not done voluntarily, or things that are done voluntarily but without any intent to persuade, can still convince. If I make an argument to my brother about why brand X is better than brand Y, I might persuade him to buy brand X. I might convince him to buy brand X. If my brother learns that brand Y is not available in his local store, he may be convinced to buy brand X by that fact. But the unavailability did not 'persuade' him to do anything.

Basically they are synonyms, but I´d say that persuade includes changing the person's way of thinking from one thing to another one, while convince is more like make someone think something without not having any point of view of the situation, like convince someone to buy a new product, and persuade someone to not to go to a party.

TO PERSUADE: 1. The international community is trying to persuade country X not to do that. 2. The police persuaded the criminal to surrender peacefully. 3. The government is trying to persuade people to stop eating so much sugary foods. TO CONVINCE: 4. All of us hope that the international community will be successful in convincing country X that what it is doing is wrong. 5. The police were able to convince the criminal that nothing would happen to his safety if he surrendered peacefully. 6. The more people become convinced that sugary foods can cause serious problems, the sooner they will eat fewer sugary foods.