I'll have to disagree, and for argument's sake, I'll base this on good ole FAT32 architecture on IDE drives. Yep, other formats will vary....
In the OS:
Quick format pretty much just wipes out the FAT table and deletes the file and directory information at the root of the partition. All the information (other than the FAT and technically the first caracter of the root entires) is still there.
A long format does the same thing then verifies it can read all of the sectors on the disk. It does not infact wipe out everything "out in the field" on the disk. Do a long format and I can still get almost everything back.
Long or Short, they are both high level formats.
And now for something completely different:
Low Level formating physically rewrites every track and sector. It will basically wipe everything out save for intensive data recovery efforts. This is usually done at the BIOS level on SCSI cards or in the good old days you'd have to jump into DEBUG and manually go to an address to launch BIOS code to do it, especially with RLL drives.
IDE drives CAN NOT be low level formatted by mortals. They simply don't have the brains, if you expose an IDE to a strong magnet and disrupt the track information the head will fly back and forth looking for a track to read. It doesn't have the circuitry or feedback servo for absolute head positioning and relies on the disk media itself to tell it where it is. The low level formatting is done atthe factory (on IDEs), some drives can be field low leveled using what is normally an excessively expensive box that makes just buying a new one a better alternative in almost all cases.
If you ever wondered why SCSI is more expensive, this is one of the big reasons.
Years ago, when I started at HP, this was my job...
Imaging, TSing and managing almost every drive that went into home products and light servers. I commited many crimes against magnetic media with those who would not cooperate. (Running drives open (and touching the platters as it's doing burn in tests just to watch them freak.), board and bios swaps to see how far the firmware could be pushed, exploring hidden tracks and reserved memory spaces, etc.)
We could LL the IDEs we were using with the external loaders. Depending on the version, some used pads or pins on the HD board, sometimes you would take the PCB off and use the ribbon directly to the head and servos. These would basically be percision devices that would walk the head up and down in a self calibration proceedure, do some math, erase the whole thing, then write the tracks again. The voltage and timing applied to the servo (voicecoil) has to be very precise because there is no feedback, it's flying blind. It would then go verify it's work. Makes sense in a very high volume operation, it wouldn't pay for itself in anything less.