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)
A binary image has only two values for each pixel, 0 and 1 corresponding to black and white (or vice versa). A gray scale image has a certain number (probably 8) bits of information per pixel, hence, 256 possible grey values.

Of course, a grey scale image has a binary representation, but the smallest size of information is not a bit, so we don't call it a binary image.

**edit** Assuming you want to convert in Matlab, use [`im2bw`](http://www.mathworks.com/access/helpdesk/help/toolbox/images/im2bw.html). If you're not using Matlab, the idea of binarization is explained on that page as well. It's not difficult to port, it boils down to comparing every pixel to a threshold value.