"So ‘left downwind’ simply means downwind, on the left of the runway, when viewed from the direction of downwind. Which will always be the the case with a RH circuit, and a LH circuit will always have right downwind".
You're going to land as much into the wind as practical, which will define the runway for landing (unless ATC instructs otherwise). Thereafter, you're going to fly a rectangular circuit pattern around that runway. If the rectangular circuit is composed of left turns, it's a left hand circuit. If right turns, right hand circuit. You the pilot must figure the turns out, if in doubt, make a sketch with arrows.
Most runways have a left circuit by default, though may be specified as right by policy or ATC instruction. A reason for a right hand circuit could be that it's a parallel runway, or a noise sensitive area underneath, or topographic feature restricting a left circuit. It is the pilot's responsibility to know which before approaching to land. Thereafter, an ATC instruction at a controlled airport could overrule the "normal" circuit, to be whatever ATC says it should be. I expect the left circuit default because the left seat pilot would have a better view for left turns.
Does that remove confusion?