For most files it looks like the "Date" field is a duplicate to the "Date Created" field.
However, if the file is an image and contains EXIF information then the "Date" field pertains to the EXIF date assigned to the image. Typically a camera will assign this field when a photo is taken. If the image does not contain EXIF information, then again -Windows appears to simply display the "Date Created" in place of "Date".
There may be other file types that contain meta data for date information, but I am not familiar with such cases.
"Date Modified"/"Date Created" pertain to the file itself, these can change if you modify the file in any way, or if you create a new copy of the file. Note that in either of these instances the EXIF date field can stay the same.
Also note that the EXIF date field is less likely to be changed as you share/move the file around operating systems and services, where as the "Date Modified"/"Date Created" are more likely to change in such scenarios.
As far as modifying the EXIF date, you can do that using perl or many other freely available tools. Heck, you can even do it in the Windows 7 explorer "properties" dialog: