The dictionary: "immigrant: a person who comes to live permanently in a foreign country". Note: permanently. But expat can be temporary.

So, if you haven't decided that you'll stay permanently in the new country, but maybe instead you'll move to a 2nd new country, a 3rd and so on, then you might consider yourself an expat, but not an immigrant. At least that's how foreign students here, seem to refer to themselves: They're here for a few years, and then will probably leave, and they call themselves "expats".

And also, what about this: If you still have your identity in your home country (e.g. the culture there?), you'd think of yourself as someone from that country: "I expatriated from Home-Country". But if your identity is in the new country, then you'd think of yourself primarily as an immigrant to country New-Country?