According to https://pillow.readthedocs.io/en/3.1.x/handbook/concepts.html#concept-modes,
The "L" mode represents grayscale here.... So it can hold any of 256 shades of Gray (includes black and white as Gray shades).
The "P" mode can hold 256 different colors like red,blue, green etc....
Convertion from one another, if you mean converting images from grayscale to color or vice versa.... Yes it is possible....
Examples: 8 bit black and white image ( technically Gray scale image)are "L" and any 8 bit color images are "P" mode..