Immigrant, not Expat: An Easy Mistake to Make
Someone who migrates, with intent to stay, is an immigrant. Someone who migrates, with intent to return, is an expat. But nobody likes to confuse the terms more than American emigrants.
It's hard for Americans to call themselves immigrants, even when they consciously move to another country with every intent to stay. The reason for that is simple: America has historically had huge numbers of immigrants, and low numbers of emigrants. To most English-speaking ears, the word "immigrant" is synonymous with "not American".
Emigration from the United States is uncommon. The history of American emigration consists largely of escaped slaves, missionaries, and communists – hardly a united enough faction to refer to with a single term, and not what usually what is meant by "immigrant". It's hard to find current numbers (the US doesn't keep count, but they do passive-aggressively publish the full names of everyone who has renounced their American citizenship). And while the number of annual US citizenship renunciations has more than sextupled since 2010, the figure includes plenty of people who can't be considered American emigrants, and remains in the low thousands. In contrast, one in seven American citizens are foreign-born (a statistic that has been true for most of the country's history). Very roughly, the ratio of immigrants to America, to American expats, to emigrated Americans, is 5/1/0.05. Contrast that, then, to the ratio of immigrants to India, to Indian expats, to emigrated Indians: 0.33/1/0.44.
Those numbers evidence that the improper use of "immigrant" has in fact been useful in American parlance. Linguistic shift doesn't happen without a reason, and appropriating a term to distinguish between the native-born population and those born in other countries (without specifying which) is reason enough for an nation built on immigration.
Americans who have permanently moved abroad should call themselves immigrants; although when the term has, for good reason, drifted to mean "non-American", getting it wrong is an easy mistake to make.