According to this, the difference in the US is that recreational model aircraft are covered by FAA Advisory Circular (AC) 91-57, while Unmanned Aerial Systems require either a Certificate of Waiver or Authorization (COA) or Special Airworthiness Certificate in the Experimental Category (SAC-EC). Operation in restricted airspace is another matter. In all cases, a pilot in command must maintain control of the aircraft (which I take to mean line of sight is required).
The other agency US unmanned aerial systems (UAS) have to contend with is the FCC. There are frequencies available for recreational RC use, and amateur radio bands, but last time I checked there was nothing for controlling a commercial UAS.