No difference. Both contractions of ‘he is not’. You can use them interchangeably.

They're both correct. I can't think of any differences in meaning. I don't know how we choose which one to use.

I agree with Dan and Tom: they are identical in meaning absolutely interchangeable. There is a very slight difference in that I think "He isn't" is used a little more often than "He's not." This may be because - although it is not rude a rude phrase at all - it is possible to make "He's not" sound a little bit rude by slurring the 's' sound so that it sounds like "He's snot" ('snot' is the type of mucus that comes out of a person's nose). But the only people who actually confuse the two phrases are usually 9-year-old boys making schoolyard insults.

No difference. Both contractions of ‘he is not’. You can use them interchangeably.