Yes, you have quoted the terminology directly. That terminology is how Marriott classifies properties for revenue purposes.

In the chart you reference, the title "Managed" would be clearer to the non-financial public if it were labeled "Franchised and Managed" in the same manner that the title "Franchised" would be clearer if it were labeled "Franchised and Not Managed". People in the business of analyzing financial statements understand that distinction.

Marriott labels the properties as they do because those two groups of properties have either a management agreement or a franchise agreement. Additionally, according to the company's 10-K filing, some of their management agreements allow the owner to revert to a franchise agreement if the owner elects to not renew Marriott's management of the property.

I'll stand by my 30+ years of SEC financial reporting in once again stating that managed properties are also franchised properties with the term "franchised" denoting a non-owned property utilizing one of the Marriott brands.