the memory card exploit is a application that is small in size which allows you to access a hdd. There are other applications which you can run from your memory card which are FAPlink, hdl dumb server, media player, execFTP, PS2menu-k, and there are a few more.......
In order to do this you need acces to a modded ps2, swap magic, or someone with a memory card exploit already set up. first you insert a ps1 or psX cd into your computer and open the system file with a text editor, than copy the number SLUS/SCUS........... down on paper then find the files on the web and edit the system file that is included with the file and change the SCUS/SLUS ........ with your number from the ps1/psX disk you used then you save a bunch of files to a blank cd. You put that blank cd in a modded ps2 and it transfers the files to your memeory card.
Then you insert a psX or ps1 disk into your ps2, put the memory card into slot 1, with a hard drive installed with the network adapter plugged into the back. And VIOLA it sees your hdd and it even formats it for you.
The differance between hd loader and hd advance is NOTHING ,both the same application witha differant visual gui