If not, what's the difference? A photographic comparison as an example would be great (assuming they are different).
As a general rule of thumb, in the modern DSLR world that is primarily dominated by Canon and Nikon, focal lengths are stated at their "when used on 35mm/full-frame body" values. Focal length is focal length, and doesn't physically change when the imaging medium changes in size, however different sizes of film or sensor do change the effective angle of view that is actually captured. Focal length is a rather useless value, all things being equal, as it doesn't really tell you much of anything about what the lens will do when used on a particular camera. The angle of view is a considerably more useful value, but that can be difficult to calculate given the factors involved. A simpler solution is to determine the angle of view "bucket" that your lens falls into for the size of sensor you are using.
On Focal Length, Angle of View, and Sensor Size
The angle of view of a lens of a particular focal length is dependent on the size of the imaging medium. On on a 35mm sensor or film (full-frame sensor, such as what you get with a Canon 1D or 5D, the Nikon D3's), an 18mm DSLR lens is a wide-angle lens. Full-frame bodies are expensive, and most DSLR's come in a variant of APS-C, or cropped-sensor, sizes. Most APS-C sensors are around 22-23mm. The smaller sensor captures less of the image circle projected by the lens, which effectively reduces the angle of view. While the lens is an 18mm focal length lens, on a sensor that is smaller than 35mm, the lens "behaves" as though it is a longer focal length. As such, the focal length ranges that determine if a lens is wide, normal, or telephoto change with the size of the sensor.
Common Fields of View @ 35mm
There are some common fields of view, assuming a full frame (35mm) sensor, that can be used to generally group focal lengths. There are slightly differing schools of thought on this, however here is a table from a well-known source, DPReview.com:
(From dpreview.com: Focal Length)
According to Wikipedia, a "wide-angle is a focal length substantially shorter than the focal length of a normal lens." A normal focal length is one which closely matches the diagonal of the image medium. In a full-frame 35mm sensor body, the sensor is 36x24mm, which is a diagonal of 43.3mm. The closest common "normal" focal length used by most manufatrurers is 50mm, which is pretty close to the 43.3mm diagonal of a full-frame sensor. (Similarly, in large-format photography, the film size is 4"x5", or 101.6x127mm, which has a diagonal of 163mm. With 4x5 cameras, a "normal" focal length lens is usually around 150mm.) While the term substantially in the Wikipedia article is not well-defined, the Wikipedia article cites 35mm and less as "wide-angle" and "ultra-wide-angle". Similarly, focal lengths substantially longer than a normal lens are "telephoto" through "super-telephoto" lenses.
Crop Factor and Angle of View
Since the field of view buckets that a lens falls into are dependent on focal length, and effective focal length is dependent on sensor size, one most first determine the effective focal length on a sensor smaller than 35mm. An easy rule of thumb can be used to calculate the effective focal length: Divide the diagonal of a 35mm sensor by the diagonal of the actual sensor, and multiply the resulting number (the "crop factor") by the focal length.
This assumes you know the diagonals of your camera sensor. The diagonal can be computed fairly easily using the Pythagorean Theorem if you know the width and height of the sensor. Pythagoras' theorem quite simply states:
This translates into the formula:
A sensor, cut in half along its diagonal, is a right triangle, and the length of the diagonal (c) can be computed as such:
If you know the dimensions of your sensor, and are not afraid of a little math, you can computer the effective focal length of any lens on any camera body, and once the effective focal length is known, determine whether it is ultra-wide, wide, normal, tele, or super-tele. As it is unlikely most people will know their sensor dimensions, here is convenient a table of sensor sizes, diagonals, and crop factors:
As an example, to demonstrate and prove the concept. The Canon APS-C sensors have a crop factor of 1.6x (most commonly stated, more accurately, 1.62x). This is calculated as follows:
APS-C Effective Focal Lengths
Now that you know the crop factor of common sensor sizes, you can compute the effective focal length of any lens you may use. Assuming the 18mm focal length of the original topic, its effective focal length on a Canon APS-C sensor (i.e. 550D, 60D, 7D) would be:
You can compute the focal range of a zoom lens just as easily. Given the Nikon 14-24mm lens:
Full Frame vs. APS-C Angle of View Buckets
The most common sensor sizes for many of the most common DSLR cameras are Full Frame and APS-C. We have a table of angle of view buckets for full frame, so it is useful to compute a table that defines the angle of view buckets for APS-C. I've used a crop factor of 1.55 to cover Canon APS-C and Pentax/Sony/Nikon APS-C:
Given the two AoV bucket tables, we can arrive at a table of common lenses and their AoV's for both Full Frame and APS-C sensors:
Visual Examples of Focal Length and Angle of View
I'll try to take some example photographs when it is light again to demonstrate the differences between super-wide, wide, normal, tele, and super-tele. (Its too dark right now to get any decent shots outdoors, and indoors I don't really have enough space to get telephoto/supertelephoto shots.)
I think so, on a full-frame body that is. It really depends on the sensor / crop factor. For most APS-C cameras, your 16mm looks like a 26mm on a full frame... and that is still wide actually :) One of the "bibles" for lens reviews, The Digital Picture, would even call the Canon 16-35mm f/2.8 an ultra-wide angle. I have such lens, and at 16mm it is very wide, with a lot of (expected) optical distortions.
Here is a shot of my office at home (below). Believe me, it's not that "narrow", but I wanted to have all walls in the frame. Only possible at 16mm.
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Generally, 18mm is considered wide-angle, but it depends on the size of the sensor. A DSLR camera with an 18mm lens WOULD take wide-angle shots, but if you have a compact digital camera or a cameraphone, where the sensor can be really tiny, an 18mm lens would look more like a 50mm lens or longer does on a DSLR.
The Micro Four Thirds system recently introduced has interchangeable lenses but a much smaller sensor than DSLRs, so the standard 14-42mm lens that comes with the Olmypus E-PL1, for example, would give a similar field of view to a 28-84mm lens on a 35mm camera (Full frame).
My experience, using the Nikon 18-70mm on my D50, is that 18mm is fairly wide for a DX camera. I only need my 10-20mm for extremely wide shots, but the 18-70 gets them most of the time. An 18mm lens on a full frame camera would be pretty wide.