I think the main difference is that persistence is often more associated with stubbornness and, while it can be good, it's not always good. It can be good "if you persist you will succeed". It means you continue to do something. Perseverance is normally more of a good quality. It also implies that something was done despite the odds being against them (despite it being hard). "He nearly gave up, but he persevered and made it through". If a marketing firm is bothering you with lots of phone calls they are being persistent (and annoying). If you contact their bosses to try and stop it, it will be difficult, but if you persevere you might get them to stop. That's what I think the difference is. However, you could probably swap persist and persevere around in the above paragraph and it would still be right, or at least make sense.

Hi There! Persistent is an adjective and it means: continuing or not letting up while pursuing something/firmly following a set course of action (He was persistent in his hunt for love.) * used to describe Perseverance in a noun form: the persistence of doing something you find challenging, even if you have a delay in results. (The perseverance he shows in his studies highlights his passion for the subject.). * used as a noun They are very similar in meaning and function, and can be easily confused!

so sorry, it's a typo. I mean perseverance and persistence

You 'have' perseverance. ... but ... You 'are' persistent.