BSL is not entirely separate from the Dangerous dogs act or Companion Animals Management Act (or dog and cat management act).
So Customs (or the Federal Government) have a law prohibiting certain imports - including 4 specific breeds of dog. Perhaps because customs and airport staff don't want to get eaten. I don't know.
I don't think any state has a separate "dangerous dog act" but most of the Companion Animal Management Acts in each state - have a dangerous dog section ie what happens if your dog acts menancing or is declared dangerous and what you're expected to do and what the fines are for letting your dog harrass or bite someone or dog or livestock or wildlilfe (not protecting your private property/land).
And when the federal law came in - most states changed their companion animal act - to make those four breeds automatically subject to the dangerous dog requirements (eg kept in secure dog run, muzzled in public etc). And then Victoria - outlawed getting them registered at all after September last year. The four breeds are subject to "breed specific law" or BSL - the BSL is any law that is specific by dog breed. It might include specifying that poodles must be clipped every second month or Labs must be hip scored - but not other breeds - eg breed specific.
And just to add to the confusion. Each council can add its own specific laws on top eg dogs must be on lead in playgrounds - or not allowed in playgrounds at all, or desexed unless the owner has a breeding permit etc. Each council has it's own set of rules. Most councils copy each other's rules so they're usually fairly consistent across one state but there are wide variations - especially in Victoria.
It's a bit difficult if you're travelling across country with your dog.
So the Breed specific legislation in all states (as best I can tell) is just a bit that says these four breeds that are prohibited imports are automatically subject to the dangerous dog restrictions (mostly must be desexed, and kept caged and muzzled etc). But the details are slightly different in each state, and radically different in Victoria.