The garden style that has historically prevailed in many English speaking 'western' countries is the so called 'English' style. In Australia the majority of settlers for much of our history (white) have been peoples from the British Isles and Ireland. Add the many others from Europe to that gene pool and it is little wonder that despite our quite different climatic conditions we have for historical and cultural reasons tended to retain a certain European aesthetic in many of our cultural endeavors. This garden aesthetic is to be found in many countries around the world who were settled by Europeans.
So what is this 'English Style' and is is actually from England? Essentially it is a blend of some open area's covered with mown grass (lawn) a few shrubs and tree's and area's large or small given over to collections of smaller more floriferous plants. Add some built structures and perhaps some manicured hedgy stuff and wallah we have the so called English garden.
It seems to me that most peoples around the world manage their outdoor spaces in pretty much the same way..be they of European origin or any other culture. The elements may be rearranged in emphasis, but ultimately the spatial management is in essence the same, or very similar.