"Secure shredding" is used to describe the process in which custody of the records is maintained at all times. From the time documents are placed in locked containers until they are shredded and baled, they are kept secure.
Documents containing social security numbers, credit card numbers, medical information and similar sensitive information must always be destroyed in a secure manner – either with your desk side crosscut shredder or in a locked secure document bin.
"Document destruction," on the other hand, is used to describe the process in which documents are destroyed in various manners including shredding, but are not necessarily locked securely from people’s view; there is limited custodial responsibility for these documents. This is acceptable for times of cleaning out your file cabinets of material you do not want the general public accessing, but are not of the importance level required for long term storage or secure shredding.