I've heard that faculty usually gets paid for 9 months in the US and you need to use your own funding to pay for the missing 3 months.
Is this situation different in the UK and Australia?
In Australia, if you have a permanent position as an academic at a University, you would typically earn an annual salary. This would typically be paid fortnightly, every fortnight of the year. This assumes you are working for the entire year (except of course for annual leave, public holidays, etc.).
Of course, there are plenty of causal academic roles such as research assistants, teachers and so on. These are often linked to the completion of specific roles. For example, if you tutor a unit, then you'll typically be paid for the amount of teaching you do and only for the weeks that teaching is occurring.
While we don't use the term "faculty" as much in Australia, I imagine when we do, it would typically apply to those academic staff on salary.
As a side note, Australian academics are typically allowed to earn additional income doing external work if their supervisor provides approval.
I don't know of anywhere other than the US that the 9 month contract system is used.
Under the US system you can (and many faculty do) typically arrange to have your nine month salary paid out in equal installments over the whole year. If you do this then any summer salary you can arrange (e.g. from research grants, teaching summer school classes, or administrative work) is "extra" money. Most faculty that I know budget to live off of their nine month salaries and then use the summer salary to invest into their retirement funds or to pay down their home mortgage or whatever.
There are some advantages to the faculty member in having a nine month contract. For example, you're free to use the summer to go on vacation or work for some other employer (lots of consulting work gets done over the summer.) Working on research contracts and summer school teaching are optional. The down side to this system from the point of view of faculty members is that there is no guarantee that you'll be able to get a full three months of summer salary.
From the point of view of university administrators, the advantage of the 9 month contract is that it helps to keep salaries down in comparison with 12 month salaries in industry. Universities don't need faculty to teach much during the summer, so why pay unneeded employees?
Note that fringe benefits (like health insurance, life insurance, etc.) cover the entire year including the summer when the faculty member is not on contract.