As others said above, the president has certain immunities to prevent constitutional crises. But that's only for the president, and it's not part of his pardoning powers (which wouldn't work here anyway).

So why isn't he going to jail for felony falsification of business records (forget the classified records case, he's not meant to be immune from that but here we are)

My point is that power is not about what the law says, it's about what people can get away with through their relations with other people.

Trump or Jones?

I agree but the cases are very different. There's not much worth comparing them. It's different kinds of corruption.

His conviction wasn't overturned, they are just delaying his sentencing because he's now going to be the president again. He's not doing it by any power of the federal gov't.

Exactly, there's no rule (certainly no federal rule) that says a guy can't go to jail just because he was elected president. So why isn't he? Because he has power that is not assigned to him by any law. He is a bully with a cult of personality that makes people fear him and/or act as his sycophants.