What is the difference between having a fat or a ntfs file system?

FAT filesystems are usually used for older operating systems.
NTFS is usually used intead of FAT because it provides more options, and better performance. With NTFS, you can set permissions for individual accounts or groups on a file, yuou can use Disk Quotas, you can Compress files automagically without the user knowing that anything happened, and you can use NTFS encryption to protect data.

NTFS isn't compatible with earlier versions of windows (It works with Windows NT, 200, XP, and onward). It's not supported on 3.1, 95, 98, ME, or DOS. Also, the older versions of Windows NT use a different version of NTFS than XP and 2000 do.