persist - to continue firmly (with deep intent) doing something, especially in the face of opposition insist - to be very firm or emphatic on a particular mattter, to demand, to steadfastly believe you are correct about something The big difference between the two is that persistance is often associated with opposition - "If you persist in talking to me in that rude tone, I will just leave." "If that cold persists, you should really go see a doctor." Insistence does not necessarily involve opposition, it is usually more of a mental attitude. "He insists on checking each package himself." "She insists on using her maiden name." "She insists that this price is incorrect."

They are two different meanings entirely. "to insist on" is more of a verbal statement. "I insist you do that work for me" is a more polite way of saying "you WILL do that work for me" - it is forceful. It means I want you to do that whether you want to do it or not. For instant if someone offers you a cake and you decline, they might say "But I insist!" "to persist in" means to keep doing something until you've achieved a desired goal. If you say someone is "persistant" it means they will keep trying over and over again until they get the result they want.