I'm not sure what you mean by the "Re" model, but ultimately the transistor does a certain thing regardless of what label we put on the circuit it is in.
For a NPN like you're modeling, you will have base current going into the base and coming out the emitter, and collector current going into the collector also coming out of the emitter. If you consider β the gain of the transistor and the magnitude of the base current 1, then the collector current is β, and the emitter current β+1. This is true regardless of the external circuit, so long as the C-E voltage is enough to keep the transistor in its "linear" region, and no maximums are violated.
Different circuit may use a transistor in different ways, but what the transistor does, and therefore its model, remains the same. At most, some circuits may exploit different regions of the transistor's operating range, which might lead to different simplified models.