In New South Wales there is the state wide comp (NSWFL), and the Swans have their own team within that comp and that is who Davis was playing for, it was just in Wagga, probably against their local (and probably pretty good) side, which would have as much importantce to the comp as the Swans reserves.
There is also the Sydney football competition which has affiliations with the Swans, but as I understand it my local team, the Pennant Hills Demons (which produced Lenny Hayes), also has some kind of affiliation with the Melbourne Football Club - when the team is in Sydney they often spend time with the Pennant Hills team and the local supporters.