There are three basic type of telescopes:

Reflector: uses mirrors to focus the light

Refractor: uses lenses to focus the light.

Catadioptrics: uses both lenses and mirrors to gather and focus the light.

With telescopes size matters! The telescopes light gathering power is proportional to its objective's surface area.
 

As an example an 8" (20cm) telescope has 4 times the light gathering capability then a 4" (10cm) telescope. Not 2 times as you  might first think.

That  means  on a clear night  an 8" scope should be able to  see magnitude 14 or better stars. That's more than 380,00 time fainter than the faintest star that can be seen with the naked eye. The best you  could do with a 4" scope would be something around magnitude 12.5 ( The lower the number the brighter the object)

RESOLUTION

The more light that  your scope can gather the more detail you  will be able to  see. This is what's called resolution. Resolution is measured in arc seconds and is  a theoretical number but it provide you  with  some comparison value.

Back  to  the 4" and 8" scope comparison. A 4" scope should be able to  distinguish object that  are 1.2 arc seconds apart. whereas the 8" and distinguish objects that  are .6 arc seconds apart. You can see that  the more light you  can gather the more detail you  will be able to  distinguish.

FOCAL LENGTH

The focal length is defined ad the distance the light travels from the objective (front lens or main mirror) to the point where it is focused. The longer the focal length the larger the image will be at the focal point. However, it will be fainter.

The focal ratio it the ratio of the telescopes focal length to its aperture. Divide the focal length by the diameter of the objective. Let say  that  the 8" scope had a focal length of 36", that  would yield a focal ratio of f/4.5

TELESCOPE TYPES:
Let me give you a few more words about the differences in telescope types.

The refractor telescope , as mentioned above, employs lenses to  they the light from the front of the tube to  the eyepiece. The objective usually consist of tow or more optically configured glass that  directs the light to  far end of the tube. These type of telescopes have the ability  to  provide  large, bright, high resolution images.

The reflector telescope has a concave mirror at the bottom of the tube which gathers the light and focuses it on another flat mirror suspended in the center of the front of the tube. This mirror is set at a 45° to  send the image out the side of the tube to  the eyepiece.

The catadioptric telescopes ( Schmidt-Cassegrain is a common type  also known as SCT) have a spherical mirror with a hole in the center at the back end of the tube and a correcting lens at the other end. A mirror is mounted on the correcting lens which  directs the light back down the tube thru the hole in the main mirror. The light is reflected at a 45° angel out the eyepiece. Because the light travels back  and forth the tube twice it double the instrument's. focal length. Using this design, a SCT with  a 24" tube has a 48" focal length.