Difference between Approach/Departure & Radar.

[Field In Sight]

What's the difference between the use of ATSU call signs Approach/Departure and Radar.

I have called up before by doing the initial call i.e.
"Hawarden APPROACH this is G-ABCD"
and the reply was
"G-ABCD Hawarden RADAR Pass Your Details".

Obviously this is because they had Radar available.

I have read that the callsign Approach is used for a non-radar procedural service, but I fly from Liverpool, who do have Radar, and it's Liverpool Approach???

Also when departing, I contact Liverpool Approach not Departure?
Is that reserved for when the Approach/Departure frequency is not combined.

Thanks