Difference between Quick Format and a normal/long Format
Both types recreate the file system structures. Depending on the platform this will include the file allocation table or the master file table.
The only noteworthy difference between the two is that a long format will check every sector on the disk for errors.
When to do a quick format
For workstations where you are installing an OS on a known-good drive, or when rebuliding a PC on a drive that was previously used as a OS with no hard drive problems. A quick format is also usually required when using a third-party device to allocate space on the hard dribes - such as a RAID array. Usually the long format will fail as the OS will not be able to 'see' every sector on the disk.
When to do a long format
For workstations where the hard drive is brand new / has never been previously used or when the hard drive is going to be used in a server but NOT in a RAID array.