What is the difference between a quick and full format?
The term formatting is used for different things.
First it is used for low-level formatting a hard disc. This includes taking the disc and dividing it into small units - the blocks, which can be accessed by the operating system. Nowadays the manufacturers configure the sector size (like 512 bytes or 4096 bytes) and low-level format the disc. Normally the user can't low-level format a hard disc anymore.
Second formatting is used for high-level formatting a hard disc. This means that the operating system is writing a file system structure to the disc. For good old FAT (File Allocation Table) for example the system would write a boot sector to the first disc sector and an empty FAT to the following sectors. Empty in this case means that all entries in the File Allocation Table are marked as unused.
High-level formatting might include scanning the disc for bad sectors (check if every sector can be read) and it might include writing zeroes to all data sectors on the disc.
When you format a disc, then Windows XP does a high level format, it writes a file system structure to the disc. When you say full format, then Windows XP also scans all sectors on the disc for bad sectors (see MSKB). Since Windows Vista a full format writes zeroes to all data sectors (see MSKB). Accessing each sector on the disc takes much more time than the quick format which only writes the blocks that contain the file system structure. So normally a quick format is what you want because it is much faster. But there are cases where you might want to do a full format.
- You might have a disc that you want to destroy or give away. If you just quick format, then the file data is still on the disc, only the file system structure (file names and Information where the files are stored on the disc) was deleted. With specialized programs someone might try to "undelete" your files - the data is still there, the task of the program is to guess/know which data block belongs to which file.
- You might not be sure if the hard disc is in a good state. Then full format is a good idea because it accesses every sector, so if any sector is bad, this will be recognized. With a quick format only a few sectors will be written to. With bad luck you end up with a successful quick format, and when you later want to write data to the disc it fails. Then you'ld probably prefer if you had done a full format that had checked all the disc right at the beginning. Of course you can always run a 'chkdsk /r' later to scan a disc for bad sectors.
You asked about risks and consistency. I wrote about the risks above. Regarding consistency there is no difference. With every format the operating system writes the file system structure and this structure is the starting point for every file system access. It does not make any difference if unused sectors are zeroed out or filled with random data.
For more information you might want to take a look at the Wikipedia Article for Formatting.
A full format checks for bad sectors on the disk after formatting. This check is responsible for the majority of the time that it takes to format.
Quick format skips this check.