Question: is there any difference between grey scale image and binary image?

Answer: 
Yes, the one is grayscale, e.g. gray scales from 0.255, the binary imange is binary, that means black(0) or white(1). 

EDIT: Convert grayscale to binary. Directly converting color images (like RGB) to binary is not that easy, because you have to handle every color channel within the image seperatly. 

Converting to binary is done using a ceratin threshold. E.g. you can say, all pixels with gray > 125 will become white, the others black.
There are several thresholding algorithm out there, but maybe the most common is Otsu. You can find it here [Thresholding by Otsu](http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/MORSE/threshold.pdf)
**Black and White** image contains only **two levels**. 

**Gray image** represent by black and white shades or combination of levels for **e.g.**
**8 bit gray image** means total **2^8 levels** form black to **white 0 = black and 255 is White**.