The distinction between a TED Conference and a TEDx event is primarily in how they are organized. TED Conferences are run by TED directly.
TEDx events are locally organized by passionate volunteers who obtain a license from TED to create an event tailored to their community. These events uphold the same spirit and format of TED, with the goal of sparking connection and conversation within the community. Organizers follow TED's rules and guidelines but have the freedom to shape the event's content and design.
TEDx events are fully independent in their planning and production, which means that TEDx organizers do not receive assistance from TED in areas like speaker selection or ticket sales. Instead, they leverage the TEDx platform to inspire local engagement and ideas worth spreading
You can learn more about TEDx events here.