The DG designation applied to most newer Sigma lenses indicates that the lens is especially suited for use with digital SLR cameras. The DG lenses feature improved (more even) light distribution from image center to edge, and incorporate the latest multi-layer lens coatings to avoid reflections of the sensors of digital cameras. This is important in digital photography, but is also useful in 35mm photography, especially when slide film is used. Lenses designated as DC are designed exclusively for use with digital cameras having APS-C size image sensors. They feature smaller image circles and often feature shorter focal lengths (e.g. 10-20mm DC, 17-70mm DC, 18-50mm DC, 18-200mm DC, etc.). The shorter focal lengths are desirable, because most digital SLR cameras have image sensors whose dimensions are considerably smaller than a 35mm negative (usually by a factor of 1.3X to 2.0X), making the lens’ angle of view equivalent to that of a longer lens on a 35mm cameras.
from Sigma web