Think the difference is that an expat makes his wealth from outside that country he migrated to and Immigrant makes money from the country they migrated to.
Rich expats are pretty much by definition not "immigrants", they're usually visiting for a few years with a fat "expat package" courtesy of the company. But these are increasingly a dying breed, and most expats are neither fat cat expats nor dirt-poor refugees, but somewhere in the middle.
Also, much of the calculator asks for things like a liter of gas or a bottle of Coke, whose price is not going change radically no matter where you shop.
Not all expats are created equal. For example, Mexicans living in the US tend not to do so well in education or the economy, dragging a lot of US national statistics down. This is because a lot of Mexican-Americans come from lower class backgrounds and not Mexico's educated elites.
The difference between an 'expat' and an 'immigrant' is that an expat made their choice from a position of strength and an immigrant made their choice from a position of weakness.
That's really all there is to it, everything else is exactly the same. Though usually people from wealthy countries would not like to be known as 'immigrants', they are expats, of course.
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