A Swap Disk for the PS2 works pretty much like "Freeloader" for the Gamecube, it unlocks the region code and in this case makes burnt games playable. However, what is different from the Gamecube and the PS2 is the way you put in the disc. With the Gamecube, you can just put the Freeloader disk, take it out and then put in the imported game in with no problem. The PS2 however is different. Since it opens and ejects from a tray, there is no way to exchange discs without pressing the eject button and thus allow the swap disk to unlock the region code. This is where the slide card comes into play. What the slide card does is it allows you to exchange the discs manually without having to press the eject button to open the tray, thus allowing you to change the discs without allowing the unlocking process to get interupted.

The difference between using a Slide Card with Swap Disks and a Modchip is that the Slide Card/Swap Disks allow you to play the games without ever opening up the console and breaking the warranty (trust me, from what I've seen, you don't want to open up the PS2. It is pretty hard to put everything back the way it was and not screw it up). So in my opinion, I would go with the Slide Card/Swap Disk method. Although I have never done this process myself (I know all this from reading about it), it seems to be the easiet way to do it.

I used the comparison with the Freeloader disk because I used it for Naruto: GNT 3 (and I'm assuming you have either used/heard about it). My reasoning for "how it works" is a bit lackluster (doesn't really go into the deep mechanics of it), but I believe I got the jist of it. Hope I could help.