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)
Yes,

A binary image is one that consists of pixels that can have one of exactly two colors, usually black and white. It is also called bi-level or two-level.

A gray scale image is a kind of black and white or gray monochrome are composed exclusively of shades of gray.