A reflector telescope uses mirrors to provide an image.  The reflector telescope was invented by Issac Newton and are also known as Newtonian or Mirror telescopes.  Dobsonian telescopes are also reflector telescopes and are named after Frank Dobson who pioneered the simple but effective Alt-Az mount that these telescopes use..

Compound telescopes use both mirrors and lenses to produce their image.  They are sometimes referred to as compound telescopes.  Examples of these include Maksutov and Schmitt Cassegrains.