Hey J,
"he's not" expands to "he is not".
And "he isn't" expands to "he is not" as well.
So there shouldn't be any difference between the two. I suppose one grammatic feature you should be aware of is "Andy's car" does not mean "Andy is car", it means Andy owns the car. You would also say "his car" as equivalent, not "he's car".
Hope that helps 🤠