We seem to agree that a maximum rate turn is achieved when maximum lift is achieved at the aircraft load limit. Practically speaking pulling light buffet at the aircraft's limiting 'g'. Only very high performance aircraft will be able to sustain this in level flight without the speed decreasing and if the speed decreases then the light buffet will no longer achieve limiting 'g', hence a need to descend and sustain the speed.
Theoretically the best radius of turn will be achieved at the slowest speed and the highest load factor, in other words if an aircraft could fly a high 'g' turn at low airspeed. Most (all?) aircraft are unable to do this so a compromise is required.
I'm not clever enough to post a graph but essentially Rate of turn is proportional to VSquared/load factor and Radius of turn is proportional to load factor/V.
So in an F16 there will be a large gap between best rate and best radius speeds and in a C150 there will be a small gap. There will however STILL be a gap!