convince / persuade
To win the mind vs. to move someone to act.
To convince is to make someone believe that something is true: The test results convinced the engineers that the bridge was sound. To persuade is to get someone to do something: The mayor persuaded the council to fund the repairs. Use persuade when the result is an action.
Examples
UseYears of data finally convinced her that the drug worked. (she came to believe it)
UseHer doctor persuaded her to start the treatment. (she took action)
AvoidHer doctor convinced her to start the treatment. (the result is an action, so persuade fits)
Dictionaries now also list convince meaning “persuade.” However, many people still consider this use an error, and they judge the speaker who uses convince this way.