They’re interchangeable, but repair is more formal whereas fix is much more common in day to day speech.

I think you can use both, but there's still a difference, I believe repair is more precise and limited comparing to fix! In exemple you can say fix a problem but not repair a problem ...

I agree with Molly...fix is more natural. It can also be a phrasal verb- to fix up /to fix something up meaning renovate, or fix up meaning arrange a date..."I'll fix (up) a time to meet".

Also, "fix any differences" would probably be used to describe mending a relationship, while "repair" would be more suitable for mending a broken machine.