This is very much Musk worship. You really think they use the exact same software at Tesla as they use for SpaceX? Is there any reasons at all to believe the programmers from these two companies have ever even met each other? Or share code via some kind of cross-company repository?
Since Musk drives product development at both companies and owns both of them, yes, I'm confident engineers collaborate between the two companies. It would be stupidity not to.