A more intuitive equatorial mount is the fork mount. The telescope is suspended between the tines of a fork on its declination axis. The axis of the fork is the polar axis. This type of mount is used for physically short telescopes, like reflectors. Refractors are pretty straight forward, optically with the objective at one end of the tube and the eyepiece at the other end.
Reflectors come in a wide variety of optical configurations.
The simplest reflector is the Newtonian named after that gravity fellow who invented it. It is a large open tube with the primary mirror at the bottom, and a small flat diagonal mirror near the top to reflect the light out the side to an eyepiece. These can be very inexpensive when combined with a Dobsonian mount. The Cassigrainian comes in several forms itself, but has a small convex secondary mirror which reflects the light through a hole in the primary mirror, so the telescope looks like a fat stubby refractor. The kind made by Celestron and Meade are of the Schmidt variant and are rather reasonable in price.