What is the difference between “Black&White” Adjustment and Saturation in Photoshop?

Black&White adjustment controls the amount of black/white in the colors, which is in a nutshell the brightness of the color, while the saturation controls the amount of color used, those edits can be performed on a specific color, or on the image as a whole.

Black and white mean the2 colors without the value of hue. 

Saturation include the values of light and dark.