I gather the main dispute here is the 'legacy' RBTU members at the Transit
Systems depots have kept their STA perks and conditions when the depots
were 'privatised', but the TWU workers doing the same job for the same
company have worse terms and conditions. And presumably, new hires at the
former STA depots are on TWU contract conditions, not RBTU contract
conditions.

Just where did this situation where 'private' company drivers came to be
represented by a different union than 'government' drivers come from?

A number of years ago, where I work two unions claimed the right to
represent people in my type of position, and the pair of them fought it out
in the courts for well over a year for 'exclusive' access before the ruling
came down that the workers could choose. Queue being bombarded with letters
claiming to better represent my interests. However, in my case, it doesn't
matter what union you are a member of (or not at all) everyone in the
job/grade gets exactly the same contract conditions.