Well I'll give it a go.
I'm a UK controller who works in class D surrounded by G.
Unfortunately, I think this whole debacle is a victim of a poor choice of wording on behalf of the regulator.
Radar Control Service with reference to VFR only for this explanation,
To a casual reader it obviously implies that you are being controlled using radar right? Wrong. What is actually means, is that a surveillance system is being used to provide a service (read assistance) inside CAS. This service includes everything you would expect from a basic service, with some additions (Wx, integration of traffic within the CTR/CTA, routing and or level 'requests', and basically anything else we can do to help. I've ordered fuel and a breakfast before now!!) as SD explained earlier, we segregate rather than separate VFR vs IFR or VFR vs VFR. A basic duty of care still rests with the controller, however, you guys can see out of the window and ultimately make the decision whether you can comply with our instructions. If not, we'll come up with another plan to fit you in the prevailing traffic situation with any risk negated to help you with your arrival/transit.
If you have never been told upon entering CAS that you are on a RCS either the controller is non conforming, OR they do not see or have not identified you on radar. Generally not best practice, and we particularly like to know what and where everything is inside the zone.
In basic terms, if you are VFR you are responsible for separation. We will provide appropriate traffic info on any other a/c that maybe in the vicinity. We may suggest a course of action to "segregate" but don't always expect it. If you can't comply with a level restriction (usually a not above) or a routing, then tell us. The original example shows a very poor attitude towards VFR in class D
Oh and the approach vs radar thing.
"ZZZZ Approach" means an approach controller is using procedural methods for the approach i.e. no radar. So you'll be flying full arrival procedures or will be VFR.
"ZZZZ Radar" guess what, means the controller is using a surveillance system to monitor your flight, so full radar vectors etc can be expected to save all those extra procedure miles (unless I'm vectoring of course
) with reference to VFR you'll just get less or no requests for your position.