It used to be the case that you’d “convince” someone that, for example, apples tasted better than oranges, but you’d “persuade” them to, for example, bring you an apple. That is, “convince” and “persuade” used to have different meanings; you would “convince” someone “of” something, or “that” something was true, and you’d “persuade” someone “to” take some action.
This distinction has evolved away — and in a relatively short time. When I say it “used to be” I mean only a couple of decades ago. By now, the dictionary definitions of the two words are almost identical and they’re used interchangeably.
It’s not that the words ever differed completely. “Persuade” appeared in English around the 1400s, and even then was occasionally used more like “convince.” Similarly, “convince,” which appeared in the 1500s, was sometimes used more like “persuade.” Really it was grammarians and people who fancied themselves the “rule makers” for English who tried, for a couple of centuries, to convince everyone that the words were more different than you might think, and persuade them to use them in distinctly different ways. Or is that they tried to “persuade” everyone, and “convince” them…?
In any case, “persuade”, which comes from the Latin word “persuadere” (to get someone to do something) has a first citation from 1450, where it was used in the sense of urging action, but as early as 1487 was found to be used for promoting a belief:
“They perswade the kyng wilfully to take his deth aftre the accustumable vsaige observed of olde”. This is from a 1487 translation of the Greek “Bibliotheca Historica,” which was a “history of the world” that ran to forty volumes!
It took longer for a citation to appear of “convince” being used to urge action. While “convince” meaning “to urge a belief” was first cited in a 1763 publication “Debates of the House of Commons from 1667 to 1694” (the go-to cure for insomnia in those days), the earliest example of “convince” urging action seems to be from the 20th century.
So now’s the time to ask yourself: are you persuaded, or is it going to take more convincing?