Good question. It differs somewhat from state to state and most of what I see on the net is wrong or at least leaves out some important details. That's part of the problem.
Wikipedia isn't that bad. Gun laws in Australia if you read it's two first sections National Firearms Agreement and Firearms categories but I'd add the following explanation to that.
The basic firearms licence is an A/B licence - for all intents and purposes A/B weapons are treated the same, making the division between those categories pretty meaningless.
And Category C licences are not that hard to get - the Wikipedia article gives the impression they are more restricted than they actually are. Same with handgun licences. Category D licences are also a little easier to get than Wikipedia implies, but that is genuinely hard.
My own summary:
We have universal licencing and registration of all firearms. Getting a basic licence (A/B) is easy as long as you do not have a recent criminal record, getting a C or H licence is doable for most people with a bit of work. Buying a new gun even if you are licenced involves navigating a lot of pointless bureaucracy that serves no purpose, but can be done. The right to self defence is complicated - you do have the right to self defence including the right to use a weapon in self defence if the threat is serious enough but there is no right to carry a weapon for self defence 'just in case' - you need to have a reason to feel under imminent and real threat, so very few people routinely carry a handgun even if licenced.
Thank You!
Sounds like they used New Jersey gun laws as a model. A carry permit requires you to "prove a need", and the proof is never enough unless you're among the "connected".