De-atomization is the anomalistic ability to break down atoms to their simplest form, which is (according to superstring theory) pure vibrating energy. By doing this, there would be no bi-products produced that would be harmful to the environment or otherwise detectable unless by intense scientific study.
Splitting the atom happens when extra particles, neutrons, are added to the nucleus destabilizing it and causing a breakdown within the substance. This results in anything from a simple fracture to complete disintegration. The possibility even exists, to take this energy and use it as a power source for other things. However, this ability alone does not grant this level of control. A secondary ability would need to be devoted to this.
NOTE: This power is currently Restricted in the Role Play.