Disney owns both companies, but they run independantly and run their own creative and production. Disney funds and distributes. There’s no brain trust at Disney that lords over both comapnies.
Marvel’s process is that Kevin Fiege is like an editor in chief. He sees the grand picture of where things should go. Individual movies are basically put together in-house by a creative comittee looking at years worth of comics. The have writers in residence who often write the first drafts. Then they find a powerhouse writer/director to come and rewrite the script to their vision and see it through to the end— all while taking notes from Fiege that address the grand plan. Marvel movies all have the exact same formula and rely on said writer/director and top notch casting/talent to make it enough of a spectacle that you either don’t notice or don’t care you’re getting the same story.
Star Wars has a similar exhibiton goal, but, as crazy as it sounds, is still finding their feet. They have a brain trust as well, with Simon Kinberg, Lawrence Kasdan, and a few others on deck to sort of plot out the big movements. From there, thus far, they take their concepts to writer/directors who have indy hits and are of the Star Wars generation. Their plan is not ambitious as Marvel’s. They are doing the sequel trilogy interspersed with Anthology stories. The problem is, they both cater to and alienate the fanbase in a way Marvel doesn’t. Marvel makes their movies out of the “best of” comic storylines. Star Wars is trying to push into the new, but at the same time be precious about their past. The Last Jedi tells us to forget the past and embrace the different, while Rogue One and Solo anchor themselves to classic Star Wars as much as possible. I don’t need to start another debate on the merits of TLJ or any other new SW movie— but whether you love them or hate them, I think we should agree the one thing they aren’t is consistant. Not that they should be doing a shared universe story leading to a big team-up movie— just that on a thematic level, every Marvel movie is the same. That is the Marvel brand, and it’s what makes it seem consistant. Star Wars is just relying on it’s recognition to define it as a brand instead of being consistant with their storytelling.
Anyway, at the end of the day, Fiege runs Marvel, Kennedy runs Lucasfilm, they hire who they want and direct the creative, and Disney is hands off as long as they make their money back (which they have on every single Marvle and SW film to date.)