What's the difference between telephoto lens and zoom lenses?

For example, the nikon 70-300 telephoto lens vs 55-300 mm lens.isn't the zoom the same? So what's the difference?

Telephoto is any lens with a focal length over 50mm. A zoom lens is one that can zoom over several focal lengths. Those two lenses are telephoto zoom lenses. However, I have a 100mm prime lens, which means it does not zoom, it is just 100mm. I also have a 17-40mm wide angle zoom lens.

A zoom lens just means it has a variable focal length - that is, it goes between two focal lengths. Those are both zoom lenses. It has nothing to do with the 'reach' of the lens, for example a 10-20mm lens is a zoom lens, but its at the wide angle focal length range. A telephoto is generally a lens above 50mm in length.

So;
Lenses can be either 'primes' (a fixed focal length) or 'zooms' (a variable focal length), so for example;
24mm lens - wide angle prime
10-20mm - wide angle zoom
50mm - mid range prime
300mm - telephoto prime
70-200mm - mid to telephoto zoom

In terms of 'x times zoom' (which is how zoom is described in point & shoot camera terms), its the longer focal length divided by the shorter, so the 70-300mm is a 4x zoom, (300/70), the 55-300mm is a 5x zoom (300/55).

After debating between Canon EF 70-300mm f/4-5.6 IS USM Lens and the 70-200 L series I decided to purchase this lens. I have been pleasantly surprised by the results. I also own the 17-85 and the 50mm 1.8 lenses and I have found that I have gotten the "most pleasing" results from this lens. The pictures have been very sharp from my 20D - even in the 200mm - 300mm range. I've also been happy with the quality of the bokeh.