Empty Trash simply deletes the file system directory reference as to where the file is. If the file system doesn't know where a file is, it doesn't see it or count is as part of the space used on the system. The file itself remains written on the drive and is recoverable until, and even after in some cases, other data is written over it.
Secure Empty Trash not only deletes the File System Pointer to the File, but then goes to the file itself and overwrites the file data on the hard drive 8 times with random data. This is designed to make the file unrecoverable and is actually written to a US Department of Defense (DoD) specification (which is now outdated). Recovery is possible, but it takes a lot of time and effort to do so. Newer tools can write over data many more times and the new DoD specification requires 37-45 passes before a drive is considered "safe".
By the way, that specification I referenced above is required for working with drive that handle classified material. The DoD used to use only floppy discs which were destroyed after use. When it came to classified computers and hard drives, the idea of destroying it when done became obsolete as well as to expensive.