Big difference between a visual circuit and a circling approach is that the circuit is flown in VMC while the circling is not VMC, i.e., it is IMC but with the required minimum visibility.
Not always as clear cut as that though.
For example, If we have 10km visibility below a cloud base of 1000 and the only way to get down below that base is an RNAV to straight in minima, would you be breaking any rules by 'circling' to land on the reciprocal runway?
Clearly this is a breach of the regulations, but one could argue that you are now in VMC and can conduct a visual circuit to the reciprocal runway. Despite having descended way below the circling minima to break clear of cloud.