The differences between the US and UK system are quite pronounced.
In the UK you tend to do just pure research, maybe with one seminar/training session to attend per week. In the US, you have to take about 20 hours of classes a week for the first 2 years, plus do your research.
In the US system, you have to have a 3 hour viva with your 'committee' of 5 academics at the end of your second year where you state your research proposal, and this is pass or fail. If you pass, it's very likely that you will go on to pass your PhD. In the UK system, you are generally reviewed, pass or fail, every year, until your final viva, which you can then still go on to fail if your research or thesis quality isn't good enough.
A US thesis also can be very short, and include your publications, whereas a UK still uses the traditional thesis format and often you will have no publications until you graduate.
UK PhDs are about 4 years, US PhDs are 5 to 6 years.
UK PhDs tend to be either completely funded, or completely unfunded, whereas in the US you may have to work as a teaching assistant to cover your fees.
I don't know about the structures in the other countries, but I believe Australia is similar to the US model.