Are "remote controlled" aircraft and "drones" the same thing? Are they synonyms for "unmanned aerial vehicle"?
Drones are simply the common name for Unmanned Aerial Vehicles. Representatives from the industry and the military use the term UAV for the aircraft and UAS (Unmanned Aerial System) for the whole system- including communication system, on ground controller etc.
In general, technical publications call them UAVs or usually UAS's and rarely (if ever) drones. On the other hand, the mainstream media refers to them usually as drones as it is easy to communicate.
The ICAO (International Civil Aviation Organization) calls them remotely piloted aircraft. However, there is a subtle difference in using this word as it means that it is being flown by a pilot (controller) on ground.
Though this may be technically true, most of the UAVs, at least those used in the military are capable of highly automated mission profiles (in fact, they depend on the controller only for weapons release) and are on the way to full autonomy.
The choice of wording is one of semantics i.e. about the meaning which is to be conveyed. For example, the nobody wants a system that goes and kills someone without human intervention. So, the USAF calls the MQ-9 Reaper a Remotely Piloted Vehicle in its official page and a UAV in press releases, but not a drone, as it has negative connotations in public mind.