To be honest I don't think Musk is in charge. I think they both believe they're in charge.
Trump is a relatively new phenomenon in politics that's developed from online discourse. He's a reactionary shit-poster of a politician. He's dominated by his self-interest, like many politicians, but he's taken that to a level that (thankfully) is rarely seen in the West. What he specialises in is outrage-driven politics. He keeps his base scared and angry because that way it makes it easier to portray himself as the saviour from what he's told them to be scared of / angry about.
Musk is a very different animal. Sure, he's ruthlessly self-interested, but he's got more principles than Trump. Musk is a drug-addled tinfoil-hatted conspiracy theorist and truly believes those conspiracies, whereas Trump just pays lip-service to them to keep his base scared and angry. Musk is honestly the scarier of the two, not just because Trump is likely to die of a spectacular heart-attack any day now. Musk is a true believer in his own bullshit and true believers have no bounds.