Newtonian telescopes are usually mounted on Equatorial Mounts, but recently a new variety of Newtonian telescope called the Dobsonian telescope has become popular. These telescopes put the Mirror close to the ground, and use an Alt Azimuth type of mount.
Schmidt Cassegrain telescopes use a spherical reflector instead of a parabolic one. This is because of the 1.25" hole in the center of the mirror.
A corrector lens is placed at the open end of the telescope, and carries a secondary mirror that reflects the image back through the hole in the primary mirror to the eyepiece.  These telescopes are very popular as the mirrors are sealed in the scope's tube, keeping them safe from damage. Also, their tubes are much shorter, making them easier to handle.