Trump's said he's thinking about cancelling govt contracts they've signed with Musk's space x. They've had a fight on social media so the world knows they aren't friends. They shouldn't have done it because they look like they're kids fighting.
It seems to me that the quarrel between Elon Musk and Trump has gone too far to be considered just a small quarrel between two famous people in the US. There is information on social networks that Trump ordered the arrest of Musk for violating immigration laws by him and his family and even gave an unofficial order to the secret services not to take him alive. In addition, Trump allegedly wants to nationalize Musk's companies - Tesla and SpaceX - in the shortest possible time. And the Russian authorities have officially confirmed that Musk has asked Russia for political asylum and may become the head of Roscosmos. We will see in the near future what is true and what is not.