Difference between two Rooting methods
Since both sets of instructions you link to consist of running some closed-source software that interacts with your phone through the debug interface, only the authors of those programs can tell you precisely what they do.

As ce4 says in his comment, the one on the XDA-Developers website exploits a vulnerability: that is, a defect in the phone's software. The defect lets a program run as root on the phone, and this software uses that to install a program permanently so that it always runs as root.

The other software could be doing anything. If it works for your phone, it probably exploits the same vulnerability, but only the author can tell you for sure.