Right, but the point is people who are generally called expats get a job offer in another country, and move because of that job.
People who are generally called immigrants want to move, and so try to get a job in another country (or maybe don't, depends on the relationship between the two countries and the status of the person.)
The expat causality is (typically) "job -> move", the immigrant causality is (typically) "want to move -> job".
The actual ordering of when the move happens and when the job is got aren't that relevant.
Also notable that there are plenty of exceptions, grey areas, regional differences, etc. involved. Which is why I don't like sweeping statements like the one I was originally replying to, because they're invariably wrong in some situation.