Why the output for the 8-connectivity and 4-connectivity for the binary image will be different?

I need to generate connected components for the binary image, both for 4- and 8-connectivity. Why both outputs are different?

[Rik]

Have a read here and here. It will greatly improve your chances of getting an answer.

For your specific case, Wikipedia has some explanation about 4- and 8-connectivity that might help you.

[Adam]

Why would you expect them to be the same? Pixels in one are connected to twice as many other pixels as in the other!

[Rik]

Which is why I assumed junnie vix doesn't fully understand the underlying concept, which is why I linked to Wikipedia.