Cowpoke, here is the long story short. Kroozer is correct, but perhaps this may help somewhat.
Defragging a drive will rearrang files in a more optimal pattern. That is to say, unfragment files that are scattered all over the drive, as well as pull the files back together & free space back together so that Windows doesn't have to skip across free space + files in order to find what it is looking.
Additionally, it may also locate files to the fastest part of the drive. While defragging, it is possible old files will be over-written, but don't count on that for a security thing, because there will undoubtedly be tons of files that do NOT get overwritten during a defrag.
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Drive wiping is NOT similar to a format. A format blanks the whole drive so that it appears clean to Windows. Usually, it doesn't remove the files, especially if you do a quick format. Doing a drive wipe preserves your already existing files, & just writes random data patters over the areas Windows has reserved as "blank" in order to erase the files that still exist from prior file operations (file moving/copying/"deleting"/etc).
When Windows marks a file as deleted, it is still there. It simply removes a few key references to the file instead of erasing it. Wiping the drive removes these traces. If your drive happens to be SSD, you will not benefit from Defrag as all areas are equi-accessible. And you will need to use your built in TRIM to accomplish data erasure.
The difference in 1 & 3 passes, is there is speculation that the more passes you do over a drive, the less likely it is that someone can recover the data. There are some who would say that 1 pass is quite secure, then there are others who would say that well, they use electron microscopy/voltage calculations (ie, if this used to be a 1 at a certain V, then if it is a 0 now... & use a software descrambler that can guestimate using voltage table levels).
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I am not sure how possible this all is, but if your wanting to be sure, you can always use more than 1 pass. But some swear by 1 pass. You may wonder why MS did not make files to secure erase once deleted, but here are a few things to consider.
* If you copied a 30 GB file to your drive, secure wiping would take at least as long as it did to copy it. "Quick" erase takes fractions of a second.
* If MS used secure erase, how would u recover data if you "accidentally" deleted something?
* If MS used secure erase, not only would it take lots more time, but your drive would wear out lots faster.