Hi Hugo,
I’m afraid you’ve got a little confused by the options for getting from Balham to Clapham Junction. The expensive routes all use the Southern line from Balham (NR) via Wandsworth Common, whereas the cheaper ones take the Northern line from Balham (LU) to Clapham North and change onto the Windrush line at Clapham High Street. Travelling via Clapham North/High Street is solely using TfL services, even if you end up on the Southern service between Clapham Junction and West Brompton only. The decider for the fares depends on which station you use at Balham.
I hope that helps, but do come back if you’re still not sure.