I think you might still be confused. The cylindrical part you circled is not the adapter. That's the spindle. The inside of the spindle has a Morse taper. The drill chuck has a Jacobs taper. The adapter that matches the Morse taper to the Jacobs taper can be removed to fit different chucks, tools, or drills. If you want to fit the xy table, the spindle would have to be replaced by the shorter one that has an integral Jacobs taper.