Check the resolution on the computer to see if it matches your t.v resolution. Or it could be that your computer is detecting it as second monitor, that would explain why you have to take a app window outside your laptop screen for it to show up on the t.v. Check the display settings and make sure that its not setup as dual monitors.
Your computer must be setup as if you were using the TV as a projector displaying the computer screen on the projector screen. I don't know how that is done on a Mac but maybe looking for directions for the projector setup might help.
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