In this drawing the top two structures have the plane of symmetry, the bottom two don't. But all are non-superimposable on their mirror images.
Your statement about R,R and S,S being the same compound is not correct, these are enantiomers, or more correctly diastereoisomers.
Qute from Wiki "The two cis stereoisomers of 1,2-substituted cyclohexanes behave like meso compounds at room temperature in most cases. At room temperature, most 1,2-disubstituted cyclohexanes undergo rapid ring flipping (exceptions being rings with bulky substituents), and as a result, the two cis stereoisomers behave chemically identically with chiral reagents. At low temperatures, however, this is not the case, as the activation energy for the ring-flip cannot be overcome, and they therefore behave like enantiomers. Also noteworthy is the fact that when a cyclohexane undergoes a ring flip, the absolute configurations of the sterocenters do not change."