Non-bleaching products normally use abrasives or chemicals and only remove surface stains on teeth.
Bleaching products work with a chemical called peroxide and can brighten your teeth several shades.
Another process employs the use of a special gel that is placed inside a flexible device you wear around your teeth for a certain period of time. After you remove the device, you must use a second bleaching agent, followed by a special light to activate the chemical action.
Mildly stained teeth usually only require one session of bleaching.