This online calculator calculates the rectangles, which will be produced by intersecting one rectangle with another. So, technically, it performs a split of an intersected rectangle by intersecting rectangle. As a result, you can get from one to four new rectangles. One important note is that the resulting rectangles are OVERLAPPING. Or we can say that they are NOT PAIRWISE DISJOINTED. This is illustrated by the picture below
This is the intention because the goal is to produce rectangles to be maximally in each direction. This is useful in some applications, particularly for the Maximal Rectangles Algorithms1 for 2D rectangle bin packing.
A Thousand Ways to Pack the Bin - A Practical Approach to Two-Dimensional Rectangle Bin Packing by Jukka Jylänki ↩