Until now I thought that focal length is just another way of measuring how much a lens zooms: The higher the number the more it magnifies, the smaller the number the wider the angle and thus the less it magnifies. The Canon 70-200 f2.8 and the Tamron 70-200 f2.8 VC USM both have the same focal length, but the canon zooms more. Reviews say that the Tamron is equivalent to a 170mm Canon. So obviously zoom and focal length can't be exactly the same. So are they two different things or is Tamron selling a 170mm as a 200mm lens?
There seem to two things here. First is your use of the word "zoom". Most people use the word zoom to mean a lens that can change focal length. As opposed to a prime lens which has a fixed focal length. So a 300mm prime lens is not a zoom lens even though it is a fairly long (or telephoto) lens. Both the lenses you mention are zoom lenses as they can change focal length between 70mm and 200mm
The second point is about the Tamron lens being more like 160mm. The important words in that review are "at minimum focus". Most of the time the Tamron will be a (close to) 200mm lens. However when you try to focus it on something very close to the camera it's focal length will change, getting down to around 160mm at the minimum focus distance. It is a reasonably common thing in modern lenses zoom lenses - the review goes on to say that the Nikon 70-200 is actually more like 135mm when focused at its minimum distance. (Note that that review doesn't compare the Tamron to a Canon 70-200 so we don't know whether the Canon lens also exhibits focus breathing or not.)
The technical terms and colloquial usage are a bit different here:
- Focal length is a technical characteristic of a lens that directly influences its angle of view, i.e. how much of the entire field of view it will project onto the sensor. Large focal length results in a small angle of view, which means the image contains less, but it's shown larger.
- Magnification is the ratio between an object's real size and the size at which a lens can project it onto the sensor. This is a function of focal length and the closest distance at which the lens can focus. Most lenses have a magnification of 0.3 or smaller: i.e., they cannot show objects at more than 30% of their real size on the sensor. Macro lenses are defined as having a magnification of 1 or larger, which they achieve by being able to focus more closely than regular lenses.
- Zoom is the ratio between the smallest and largest focal lengths in a lens where it's variable. It's often interpreted as "how much larger than the naked eye can the lens show something," but that is only true if the lower end of the focal length range is equivalent to the angle of view that the naked eye has, which is equivalent to what a full frame camera shows with a 50mm lens. There are wide angle zooms that show things "smaller" than the naked eye even at the upper end of their 2x zoom range. So the zoom factor by itself is meaningless without knowing where it starts.
- Crop factor is the ratio of the sensor's size to a full frame sensor that has the "standard" 35mm size. This is important because a smaller sensor shows a smaller part of the image the lens projects, which has the same effect in many ways as using a larger focal length. A common sensor size is APS-C, which is 1.5 times smaller than full frame, which means that a 50mm lens on an APS-C sensor will result in the same angle of view as a 75mm lens on a full frame sensor. Which is why focal lengths are not directly comparable between cameras and you'll often hear people talk about "35mm-equivalent focal length" when computing angles of view. It's also the reason why compact cameras can be so compact: they have much smaller sensors, which means that for the same angle of view they can use a lens with a much smaller focal length, which means the lens itself can be much smaller (and is cheaper to make).