There already is a question about moving an app running in fullscreen between physical devices: Move a full screen app to second monitor – Mission Control can do that. However, is there also a way to quickly move a single tab from an app running in fullscreen mode to another display?
Safari, for instance, offers an “Open tab in new window” command in the context menu, but that opens on the same monitor. Mission Control does show all independent sub-windows of running apps, but not dependent tabs. Dragging the tab only works if the second screen is showing a Desktop (not another fullscreen app) and will make the tab windowed.