A color gamut is defined by the range of colors a particular device like a digital scanner, display, camera or print device can capture, display, or print. Another way to look at it is a color gamut is a color range - or dynamic range for you photographers. Each device has a specific color gamut. The image is a screen capture from the OS 10.4 ColorSync Utility. It shows the bottom part of the gamut where most of the shadow information is present. Profiles such as sRGB, Adobe RGB, ProPhoto RGB, SWOP CMYK, GRACoL CMYK, all have color gamuts. Your scanner, display, and output profiles all have color gamut.
A color space is a relationship between the digital files values (RGB, CMYK) to actual appearance (CIELAB). Color space is related to vision and is defined with any color model. RGB values have no real meaning unless they are mapped to appearance, in most cases CIELAB. A color space links numerical values in a file to numerical values related to human vision.