That image shows the normal Windows XP format dialog box.
I thought there was only ONE kind of formating, but maybe I'm wrong
It depends what you mean by formatting. It can be applied to a new partition or disk or an already existing one. It is a process where everything on the disk or partition is blanked out and a new filesystem is created. This filesystem can be one of a number of different types: FAT12, FAT16, FAT32, NTFS, Ext2, ext3, ReiserFS, and I daresay some more.
The important point is that, essentially, afterwards the disk or partition is BLANK. Everything on it has gone.
Sometimes specialist tools can recover the information, sometimes not. It depends what you want to do. If you want to re install an operating system, a simple format is fine. If you want to dispose of the computer and you are worried about people restoring your data and looking at private information, get a secure file deleter program.