I am teaching a Centre College class on Australian National Identity in Australia this month.
Today we went to Melbourne's fine Immigration Museum, located in the former Customs House. We talked with Georgie Meyer, the director of public programs who led our tour and answered our questions, about who the museum served. Most of the local adults who visit are from British and other European descent. The more recent immigrants, from Asia, the Middle East, and Africa, are very unlikely to come on their own.
What I take from this is that the social category "immigrant" is a status between "newcomer" and "old stock descendant." Groups thought of a original settlers are founders, not immigrants (Samuel Huntington says as much, talking about the U.S.). On the other end are groups in which the original immigrant generation is still alive. They don't go to the Immigration Museum to hear their story, they go to the [ethnic] Cultural Center to live their story.
Immigrant is not just a temporal status, though. An immigrant group is assimilated into the "pre-Australian" path. They are part of a larger category, defined not by where they came from, but by what they are about to become. Recent migrants might go back home. Immigrants, on the other hand, can be seen, in retrospect, to be here to stay. Immigrants are migrants turning into Australians.
This insight applies to the United States, and other settler societies, as well.