When radar services are being provided, you, as the pilot will be informed by the radar controller using your call sign and the phrase ‘radar identified’ or ‘radar contact’. What this means is that the controller has positively identified your aircraft on their screen, and they will be monitoring your progress based on the clearances that you have been given. In this case you are responsible for your own terrain clearance.
If the controller needs to alter your flight path, for whatever reason, you will be advised that you are ‘identified and under radar control‘ followed by the necessary instructions. In this case, if you are on an IFR flight plan, then ATC becomes responsible for your terrain clearance when you are receiving vectors.
In uncontrolled airspace, air traffic services still makes use of radar, but will only offer an advisory or information service at the discretion of the controller. If you are flying from a controlled airspace where you have been under ‘radar control’, to an uncontrolled airspace, you can safely assume that you are no longer under radar control even if the controller does not inform you as such.
Always remember that radar is there for your safety. Filing a flight plan and obtaining a transponder code (SQUAWK) will enable the controller to know who you are and where you are, should require assistance. Knowing exactly what radar phraseology means will ensure that you respond correctly.