Welcome to the wonderful world of flying, where learning all the abbreviations and regulations is harder than learning to fly!
Ok, I'll give it a go. JAA is the Joint Aviation Authority, an authority which sets guidelines which a number of European countries have agreed to include in their own regulations. JAR is the Joint Aviation Regulations, i.e. the regulations which the JAA has come up with. The two phrases are used pretty much interchangably, i.e. a JAA license and a JAR license both mean exactly the same thing.
The CAA is the Civil Aviation Authority - the UK ruling body, which is responsible for all the aviation regulations in the UK. The CAA has signed up to the JAA, so all of the UK rules comply with the JARs.
The FAA is the Federal Aviation Authority - the US equivalent of the CAA. The FAA is not connected to the JAA at all - the JAA is a European body. The same goes for Australian authorities - not connected to the JAA (or FAA) at all.
Ok, hopefully that tells you what each one means. But it doesn't help you figure out what to do.
If you want to work in the UK, flying UK-registered aircraft, you'll need a JAA license. Under the JARs, you can fly any JAA-registered aircraft with an appropriate JAA license from any JAA country. So you don't need a UK license - a German one would do just as well. The only problem is that I don't think there's anywhere in Australia which is authorised to train you for a JAA license. If I'm wrong, I'm sure someone will correct me. The CAA website will give a complete list of everywhere you can get a UK license.
So, if you're looking to train in Australia, you'll probably need to get an Australian license. Then you have to go through the hassle of converting that to a JAR license - which isn't easy. I don't know all the details, but Redsnail has done this conversion, so she'll be able to help you out with more detailed advice.
Basically, it's going to be even harder for you than it is for most of us, unless you can get to Europe to do your training. Sorry.
Anyway, hope that's helped you understand the situation a bit better. Good luck!
FFF
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