The difference lies in their optical construction. The refracting telescope uses a system of lenses, while a reflecting telescope uses a system of mirrors.

A refracting telescope achieves its best in observing bodies that show high emissions of light, such as planets or stars, as it gives more detailed images and with a higher contrast, than a reflecting telescope. It may be used for =ormal observations, too, as it could become a powerful spyglass, with the purchase of an optional accessory called "image rectifier".

The capability to receive more light (as it's usually greater in diameter) makes the reflector ideal for observing objects with low light emissions, such as nebulae and galaxies. The reflecting telescope has some advantages in astronomical photography, too.

Essentially, they are the lens diameter, the focal length and the mount:
-LENS DIAMETER (D): this is the most important element, as it influences the telescopes' capability to gather light and give bright images. Doubling lens' diameter (in millimeters) we get the highest possible magnification. 
-FOCAL LENGTH (F): this is the distance from the object to the focus. The ratio between the focal length of the telescope and the focal length of the eyepiece supplies the magnification.
-MOUNT: this is the support, that joins the optical tube to the tripod. Beginner telescopes have got an altazimuth mount, that allows simple movements. Medium level telescopes have got an equatorial mount, that allows to follow heavenly bodies during their movements across the sky. Professional telescopes have got an equatorial mount with a polar spyglass, which is useful to make easy astronomical photography.

The quality and quantity of objects we can observe depend mostly by lens diameter and focal lenght, which determine the brightness of telescope, and by the magnification power, too. Observing Saturn, for example, fith about a 80 magnification, the planet lies in a long field without details; with a 160 the planet shows surface details and its largest satellite, Titan; over 200 the planet shows many details, such as the shadow projected onto planet's rings and few of its satellites.

The most useful accessory is the motor, which allows to follow automatically the =eavenly bodies. This is indispensable when the telescope is used for astronomical photography. Some =elescopes are motorized  in right ascension only, while others on both axis, right ascension and declination. For ideal performances we recommend to purchase supplementary eyepieces, without exceeding a magnification equal to the double of telescope =iameter in millimeters. 
Sometimes, another useful accessory can be the Barlow lens, that doubles the magnification of each eyepiece (e.g. =ransforming a 80x eyepiece in a 160x).
Finally, an image rectifier, that allows a terrestrial use of the telescope, is also recommended.

Even a simple 60mm (2”.4) n diameter model allows photography of the Moon and other planets at low enlargement. With 114mm (4”.5) in diameter, it's possible to photograph the most brilliant nebulae and galaxies. 
A normal reflex camera is enough for this type of photography; it can =e connected to the telescope with a photo =dapter plus a T-2 ring. If photos require more than few =econds of exposition, it's necessary a motorized mount, =n order to prevent blurring. Each model of =elescope with a diameter superior to 114mm allows to =hotograph a great quantity of heavenly objects.

For the newcomer to astronomy, the ideal choice is a 114 mm (4”.5) in diameter =eflecting telescope  or a 70 mm (2”.8) in diameter refracting telescope . These instruments provide the best ratio price/quality and allow the observation of the majority of bright heavenly bodies. These models =ave a mount that can be motorized, too. They are easy to use and affordable for everyone.