SFO Controller described a confused passing situation during visual side-by operations to Runway's 28; suggesting increased communications between all the participants is needed to clarify procedures.

Narrative

A B777 advised in on frequency; traffic off of their left was passing when they were told they would stay behind. I asked the B777 to advise intentions. They said they were good if I was. I advised maintain visual separation from the traffic and they acknowledged. The A319 checked in advised 'for what it's worth' they were told each were maintaining visual separation; no mention of not passing. The B777 said; 'That is just what I was told.' I advised that they were on separate frequencies and that I would report the occurrence. This is a convoluted issue and there is way too much ambiguity amongst the participants. We know that aircraft have gone around because of not only TCAS RA's; but also because they did not want to pass or be passed on final. At some point there needs to be a repair to this process; I just don't know how it will be accomplished or who entirely it will involve. I suggest a meeting in a relaxed atmosphere with controllers and management from NCT and SFO and pilots from the companies as a starting point to get all of the issues on the table collectively. Once the points are known; start focusing on a long term solution based on the feed back received.