Frames of reference do not depend on how you or me define them.  You
missed something in learning about relativity, but maybe this will
help:  SR has to do with frames of reference in which there are systems
moving at constant velocity wrt each other.  GR has to do with systems
that are accelerating wrt each other.  In SR, the inertial systems are
moving at CV within their FoR.  However, because everything in the
universe is in motion, the systems inside an SR frame only APPEAR to be
stationary wrt each other.  In fact, they are are both moving at the
same speed and in the same direction.