As far as I'm aware the MoD Police (MDP) or 'MoD Plod' are part of the Police. However, there are MoD Police also serving in one of the tri services, which are also MoD Plod, but only concern themselves with military issues and not 'civilian' issues. They regularly pass things over to the 'normal' Police Very confusing.........
In essence you have;
MDP = Police
RAF Police = Serving RAF personnel
Army Police = Serving Army "
Navy Police = Serving Navy "