If you get talked into something, you've been persuaded. If your friends try to persuade you to swan-dive into a dangerous ravine, it's time to find some new friends.
To persuade is to get your way — win the argument, convince the group to see your favorite movie, get your parents to let you borrow the car. You persuade with language, with a carefully constructed argument, and with the strength of your conviction. The word is sometimes used tongue-in-cheek to describe the very opposite of a carefully worded argument. A movie gangster might "persuade" people with the gun he keeps tucked in his pocket.