No, WhatsApp does not own Messenger., Facebook completely owns WhatsApp. Facebook purchased WhatsApp from its co-founders, Brian Acton and Jan Koum for $22 billion. Yes, that’s billion with a “b”. Both of these original co-founders initially joined Facebook but recently left. Acton left in September 2017 and Koum in May 2018.
Both men basically left because they disagreed with Mark Zuckerberg (Facebook CEO) and Sheryl Sandberg (COO) over how Facebook wanted to manage data privacy and allow advertising on WhatsApp. Acton and Koum had to stay with Facebook until November 2018 to fully vest their shares and they lost a lot of money by leaving early.