There’s no story connection between the two, and obviously, he and Peter’s relationship will be different.
For those who are confused, it’s like he’s basically the Spider-Men in Into The Spider-Verse.
They’re all the same type of hero, but also different.
Now, this may cause some to jump to bizarre conclusions, which is why Marvel’s Kevin Feige got ahead of it (via Screenrant) and confirmed this Jonah Jameson is a “completely different” character than the one from the Sam Raimi films.