There is no difference. Both Australia and the United States (and all English-speaking countries) now use the short scale:
Until the 1970s, the UK and Commonwealth (including Australia) used the long scale:
UK officially switched to short scale in 1974 (Treasury / PM Harold Wilson). Australia followed suit in government, finance, and media shortly after. By the 1990s, short scale was universal in English.
Many non-English European languages still use long scale:
Bottom line: In any modern Australian or American context — finance, news, science, government — "billion" = 1,000,000,000 and "trillion" = 1,000,000,000,000. No conversion needed.