Q: What's the difference between "DX" and "FX" lenses? What makes lenses "made for digital" or "digital-only"?
A: DX lenses project a smaller image circle, so they cannot be used on full-frame cameras or film cameras without vignetting. On a given sensor, there is no difference in field of view between an FX and a DX lens of the same length.
Camera manufacturers make DX (or equivalent) lenses which can only be used on crop-factor ("DX" or "APS-C") camera bodies without vignetting. They make these lenses because they can be made cheaper and lighter, and because in the case of ultra-wide lenses like the Sigma 10-20, trying to design an FX version would be impractical.
Except for (maybe) the weight reduction, and often the difference in price, there is no benefit to the consumer in buying a DX lens. There is no harm, either, unless you plan to upgrade to a full-frame body or add a film body, in which case you should stick to full-frame lenses.
The field of view on a DX lens is not different from the field of view of a full-frame lens. Many folks are confused about this because, frankly, of marketing by lens manufacturers. The only difference in the content of the image is that on a full-frame body, DX lenses will vignette.