Just to add some clarification and detail to what others have replied. There were actually TWO mergers...
Several years ago, Marriott International, Inc. (NYSE ticker: MAR) purchased Starwood, bringing the Westin, Sheraton, St Regis, and many other hotel brands under the Marriott International umbrella. Marriott International now owns and operates 30 hotel brands. Here is a list
https://www.marriott.com/marriott-brands.mi Last fall, Marriott International completed their integration of all 30 brands into their new loyalty program, called Bonvoy. The Bonvoy program replaced Marriott Rewards and Starwood Preferred Guest (SPG). At about the same time, they consolidated all of the old Starwood brands into the Marriott.com reservation system, so now Marriott, Westin, Sheraton and all of the other brands in the linked list above can be booked on Marriott.com. It's one basically seamless system with 30 different hotel brands. The important thing is this is primarily hotels, NOT timeshares.
The timeshare side is different...Marriott and Vistana/Westin/Sheraton timeshare owners do get to participate in the Bonvoy hotel loyalty program, and developer-controlled timeshare inventory is rented on Marriott.com, but that's the extent of the overlap between hotel and timeshare.
Both Marriott International and Starwood had previously sold/spun off their timeshare business into two totally separate, independent companies. Marriott Vacation Club has been operated since 2011 by a new company called Marriott Vacations Worldwide (NYSE ticker: VAC). Starwood also sold off their timeshare operation several years ago, selling it to Interval Leisure Group (ticker: ILG), the same company that operated Interval International and Hyatt Residence Clubs. In 2018, an activist investor group that owned a large stock interest in ILG pressured ILG management to sell the company to Marriott Vacations Worldwide (VAC). In September 2018, that deal was consummated, so now, Marriott Vacations Worldwide manages Marriott Vacation Club, the Vistana/Westin/Sheraton vacation clubs, Hyatt Residence Club, and Interval International (as well as some smaller operations like VRI, Trading Places, and Aqua/Aston).
But as of right now, Marriott Vacations Worldwide operates each timeshare system separately - Marriott Vacation Club, Vistana/Westin/Sheraton, and Hyatt Residence Club are still three separate and distinct programs. There is no meaningful integration from an owner perspective at this time. The executive management of Marriott Vacations Worldwide has told investors that some sort of integrated program is being developed for possible 2020 implementation, but they have yet to provide details. They are conducting an investor presentation at the New York Stock Exchange next Friday, Oct 4, and have promised a few more details on what the combined program might entail during that presentation.
So as JohnPaul said, if you are buying Westin, at least for now, you only need to be concerned with the rules and and procedures used by Westin Vacation Club.