Yep, all those forms of relativity are required, because it ends up with the fact that any experiment performed in an inertial FOR will not determine whether that frame is moving or still (without reference to a fixed outside point), and then also the fact that if the aether existed and was stationary in space, then you could perform an experiment that measured the speed of light to determine whether you were moving or not - hence both the definition of relativity as the inability to distinguish between motion and lack of it in an inertial frame, as well as a recourse to the fact that the basic laws of physics (and hence principle of relativity as defined above) hold in inertial frames, are useful.
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