What’s the difference between licence payments and public lending right payments?

They are entirely different. PLR is a government programme designed to compensate authors and publishers for the lending of their work to a reader at a library.  A licence payment remunerates for copying that takes place after a work has been purchased by the user, but where it would be inefficient for the licenceholder to purchase multiple copies and similarly inefficient for the rightsholder to administer many permissions requests from the licenceholder.