Demagnetization is the removal of a permanent magnetic field from an object. Such as the "degaussing" of a CRT to remove color shifting, or the erasing of a magnetic medium (tape, floppy...).
demagnetism is when you remove the magnetism from certain magnetic objects causing magnets not to attract to metal anymore or as strong as it once did
Thing made of iron, or iron-like metals can become magnetic. If you don't want them to magnetic you can do things to them to make them give up their magnetism, and that's demagnetizing.