Flat Black vs Process Black
Flat black is composed of simply dots of black toner. There are no other colors mixed in, so it's color profile is C-0, M-0, Y-0, and K-100. This black is also known as standard black and is mostly used for text. When designers use this black for large areas of coverage in a logo or graphic it can appear washed out and almost grey. To solve this problem the other colors can be added to the mixture to create a deeper, richer black that appears as a true black on paper.
PhotoShop® Black is the default black in Adobe's Photoshop. This black includes a combination of all four toners and has a color profile of roughly C-85, M-85, Y-80, K-100. Since this shade of black uses all four colors, it's also known as a process black. By adding in the additional colors, this shade of black takes on a richer, deeper appearance, and provides a much more satisfactory result for areas of full black coverage.
The final shade of black we're going to highlight is Designer Black.
Designer Black is a process black like Photoshop Black, but has a slightly different color profile and is one of the shades of black most commonly used by professional designers. Designer black is composed of the color profile C-70, M-50, Y-30, and K-100. This shade creates a very deep, rich black that is very flexible and prints well on many different papers. This color profile can also be adjusted based on the designer's needs. By adding magenta and yellow the black takes on a warmer feel, while adding more cyan makes the black appear cooler.
For Andrew's complete list of blacks and how to use them see his post here.