Actually, that is not the case.
I don't think we're actually disagreeing. The swingover can be implemented in two ways: you describe them well, though the first example (circling approach) would serve the purposes of the question better if it were "Cleared VOR 13R Approach, circle to land Rwy 13L." The second (visual approach) would entail "cleared visual approach 13L" at some point on the 13R approach.
I suspect that rarely is either phraseology used explicitly, otherwise the answer to hetfield's question would be obvious, wouldn't it? More likely it sounds like:
"Bigbird 123 can you accept 13L"
"Affirm, Bigbird 123"
"Bigbird 123 runway 13L cleared to land"
Which case is that? If it's a visual approach, what precautions have been taken to ensure "that the meteorological conditions are such that with reasonable assurance a visual approach and landing can be completed", which is a requirement of the visual approach. The pilot has not explicitly accepted a
visual approach.