Bluesky started out being owned by Twitter (pre Musk), but became a completely separate company (also pre Musk). Somewhat like Mastadon, it is intended to be decentralized. It’s still in beta, so it’s not freely open to the public yet - you have to get an invitation from someone who already uses it.
How do they plan to make money? “We’ll be publishing a blog post on our monetization plans in a few weeks, and we’ll share more then” according to Emily Liu, part of the Bluesky team.