The equivalence principle simply states that freely falling frames are equivalent to a purely inertial frame independent of gravity. Similarly a frame that is accelerated and one on the surface of a gravitating body are equivalent:
we ... assume the complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system. -- Einstein, Albert (2003). The Meaning of Relativity.
Departures come about for two reasons. The weak EP is a form of Galileo's principle, and it says the motion of a particle in a gravity field is the same as on an accelerated frame. This insures Galileo's observation on the independence of mass of a body with respect to its motion. With the weak equivalence principle the main departure is due to tidal forces and the radial direction of gravity. so the WEP requires that the size of the frame in a gravity field, say the dimensions of a lab sitting on the surface of a gravitating body, be very small relative to the dimensions of the gravitating body. The Einstein EP (EEP) says that any local non-gravitational experiment in a freely falling laboratory is independent of the velocity of the laboratory and its location in spacetime. This is the inertial idea of being in a freely falling frame, such as the infamous elevator. Again if this frame falls through a region of a gravity field so that tidal forces are apparent there are departures. The strong EP (SEP) says that the velocity of the frame relative to any outside frame, such as a distant coordinate system, is not a determinant of the measured physics on that local frame. There is again locality of measurements required to eliminate tidal forces. This means that gravitational physics is purely geometric. This is "strong" because it makes reference to regions of spacetime that are removed from any local frame.
When it comes to the rotating frame and the EP, we have certain stipulations that are required. Certainly for the WEP and EEP we require that the dimensions of any local frame be small. This holds for the SEP as well, but we have another stipulation that physics in the lab frame be independent of motion relative to the outside world. This does not happen with the rotating frame. One clear departure is the Coriolis acceleration 2ωxv, which in the rotating frame is rather apparent if there is some motion of a particle relative to the rotating frame. An observer on a frame which observes motion of a freely moving particle as cycles or circles, with no central gravitating body present, suspects then that they are on a rotating frame. As a result the additional caveat for the SEP with rotating frames is that the motion of a particle not under any local force in that frame must have a small velocity v