From Wikipedia
Telephoto:
In photography and cinematography, a telephoto lens is a lens whose focal length is significantly longer than the focal length of a normal lens. For a 35 mm camera with a 36 mm x 24 mm format (43.3 mm diagonal), the normal lens is 50 mm and a lens of focal length 70 mm or more is considered telephoto. On the 6 cm x 6 cm format (84.9 mm diagonal) (120 film) the normal lens is 80 mm, and focal lengths above 100 mm are considered telephoto.
Telephoto lenses are best known for making distant objects appear magnified. This effect is similar to moving closer to the object, but is not the same, since perspective is a function solely of viewing distance. Two images taken from the same location, one with a wide-angle lens and the other with a telephoto lens, will show identical perspective. Telephoto lenses also have less depth of field at a given aperture than shorter lenses.
Zoom lens:
A zoom lens is a mechanical assembly of lenses whose focal length can be changed, as opposed to a prime lens, which has a fixed focal length. They are commonly used with still and video cameras, some binoculars and telescopes, and other optical instruments.
Zoom lenses are sometimes described by the ratio of their longest and shortest focal lengths. For example, a zoom lens with focal lengths ranging from 100 mm to 400 mm may be described as a "4x" zoom. The term hyperzoom is used to advertise zoom lenses with unconventionally large focal length factors, typically more than 4x and ranging up to 10x (e.g. 35 mm to 350 mm) and even 12x.
Photographic zoom lenses should not be confused with telephoto lenses, those with large focal lengths. While many zoom lenses provide telephoto capabilities, others are wide-angle zooms, that is, they have shorter than normal focal lengths, and still others are trans-standard zooms covering a range from wide-angle to telephoto.