They only manage ~130 specific properties within those brands (their website is hot garbage so I’ve provided an alt link).
Sometimes a brand will own the property, but hire an outside company to manage it, other times the mgmt company owns and manages the property, and even more other other times, the mgmt company will own the property, but the brand is (still) under contract to manage the property from the previous owner
If you’re in the market for something specific check out Project Farm on Youtube. He does a pretty good job of putting whatever he’s reviewing through its paces - sometimes I watch his videos for stuff I know I’ll never buy