It is all but impossible to completely remove data from a hard disk.
Deleting a file for example does no such thing. It simply hides the file from the operating system so that you can no longer see it. There are many utilities that can restore deleted files successfully.
Erasing and shredding are, as far as I'm aware, the same thing. This is a method of overwriting the area on the disk where the file is with random data in order to make it unrecoverable via programs mentioned above.
Unfortunately there are then other "forensic" type programs that can recover data that has been overwritten several times.