Explain the difference of grayscale and black and white?

Greyscale and B&W are the same thing. There are several ways of converting a colour picture to B&W in Photoshop or similar. Greyscale is probably the worst of them. Grey scale dumps all the colour information and leaves Photoshop with very little to work with. It is the same as selecting the Red channel from the channel palette, but the Blue or Green channel might be better. The best way to convert is just to desaturate the image, this leaves the colour information in the file which is useful for selecting certain areas of an image by colour, for instance you can darken or lighten just the red parts or the blue or green or cyan etc. etc. you get the idea, so you can control which parts of the image are which tone of grey. If you look at the histogram on any of the masters of B&W like Ansel Adams you'll see that nothing in the image is totally white (burnt out, no detail) and nothing is totally Black (again no detail), so the best B&W images actually have no Black and no White in them! Because that would mean no detail and detail is what B&W is all about.