Thanks in part to Photoshop, duotone is also a generic term for images using a color-separation printing scheme. Normally CMYK (Cyan, Magenta, Yellow, and Key (blacK)) separations, whereas a duotone would be two separations, and can be of any ink color (in offset printing).
Duotone color mode in Photoshop supports between one and four colors of ink. Because home inkjet printers are far better at printing full-color images than black-and-white, many photographers use Photoshop Duotone processing to improve their greyscale prints.
Photoshop's Duotone mode is also commonly used for creating sepia toned prints, using black and yellow inks, sometimes with a third color.