This my assumptions based off logic and experience, please correct me where I am incorrect...
Defrag Drive (files and free space)
Defrags files then free space. ( Not sure about this order. )
See below for more info about each.
Defrag Drive (files only)
This is the option for a quick defrag, it takes the files that have most recently been written or moved on your partition, and place them in contingent slots of free space.
This is useful for a Gamer or Average user who installs and uninstalls select applications often, this will arrange newly installed program files and game files in such a fashion that they are accessed/read more efficiently than that of their fragmented state. ( This should be used FREQUENTLY )
Defrag Drive (freespace only)
This is less effective than the one below it, and it creates larger contingent free space without breaking files into fragments.
This is useful for long term performance, if you defragment seldom. You should compliment this with a Quick File Defrag.
Defrag Drive (freesapce only - allow fragmentation)
This is effective method of creating large contingent free space, as it will break files into fragments in order to do so.
This is useful if your current set up ( on said drive ) is your 'least important stuff' and it will all be compacted into as tight space as possible, making for lots of "unfragmented" free space.
Defragmented free space is used for long term performance. This should NOT be complimented with a Quick File Defrag, as it defeats the purpose of allowing fragmentation.
Defrag Folders
This is a thorough file/folder defrag as opposed to a files only defrag.
See Defrag Drive (files only)
Defrag Files
This will only defrag files that are specifically specified, and will not search folders for more fragmented files.
See Defrag Drive (files only)
Check Drive for Errors
This is basically a disk check provided by Windows for File systems, it detects errors in the way the file system is set out and indexed, and it attempts to repair these errors.
Use this after you encounter a BSOD or other system crash whilst performing a intensive writing task such as defragmenting. ( A system crash during defragmentation could lead to several corrupt files and a fragmented partition, the former being a real issue. To rectify this issue, you should use a check drive for errors when ever a defragmentation is not stopped correctly, by a power out, disconnection of harddrive or system crash etc. )