A reflector is any object that has the ability to "bounce" light back at an observer. Or said differently, it is anything that causes light to be magnified. The most common reflectors are found on bicycles, cars and roadways. A mirror is a surface which reflects enough light back that objects are clearly visible in them, such as personal grooming mirrors. While "reflecting mirror" is not a common term, I believe you are talking about highly polished and engineered mirrors that are used in long range telescopes as well as satellites. These mirrors have much greater reflective ability than ordinary mirrors and far greater cost. They can also be engineered to specifically reflect light other than visible light, such as ultra-violet or infra-red light, for scientific purposes.

A reflector is not a mirror, it's a little plastic thing that is often put on streets or on bikes that reflect light. These are reflectors: http://www.toolsandleisure.co.uk/ekmps/shops/toolsandleisure/images/stick_on_reflectors_%28600_x_345%29.jpg We would never say "reflecting mirror" it sounds strange. I hope this helps! :)