The difference.
A Circling Approach is an instrument approach to the circling minima followed by a visual circuit (provided all the parameters are met), to land on the OPPOSITE runway. Airports may have restrictions on this due to terrain, built up areas etc. So Mikewil, your RNAV to the minima then a 'visual' circuit is essentially a circling approach, however these are Non Grata as stated.
If you were to land on the opposite runway and there was an RNAV approach provided, surely this would be your best option in the first place.
A visual approach is an approach with no Nav aid reference.
As far as my cheaper remark is concerned, I have to admit it is cheaper for the provider rather than the user.