Persistence and perseverance are very similar in a lot of ways but there are a few subtle differences.
Persistence most of the time have negative connotation, (Negative vibe, feeling) being stubborn despite evidence to the contrary. It is used when people are chasing something which have very low chance succeeding. For example he persist with gambling even though he knew his chance of winning was extremely low.
Perseverance have positive connotation ( give positive vibe, feeling). Your goal is much more realistic if you keep at it. For example you want to be Brain Surgeon. You will have to persevere with many years of studying and difficult exams. Getting six pack will require many many months of exercise, good diet and application (Perseverance).
Perseverance can make a positive change in our situation, makes us strong. While persistence can help us or destroy us.
E.g: - He persevere with his studies despite all difficulties and eventually he became brain surgeon. Got it
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