Persistence and Stubbornness are just different words for the same personality trait. The former is used when looked at a positive light while the latter is used in the negative.
You're persistent if your project succeeded but you're stubborn if you keep at it despite unfavourable outcomes.
The way I see it, persistent founders keep looking for evidence and adapt / adjust course based on what they learn. Stubborn ones just keep going, even when there are clear signals that it's time to step back and refocus.
I would say that you are persistent if you keep getting rejected but keep improving but using feedback and you would be stubborn if you don't change a thing while keeping being rejected.
You're persistent if your project succeeded but you're stubborn if you keep at it despite unfavourable outcomes.