The "e" in emigrate is short for "ex", which means "out". You see it in words like exit (to leave), expire (out of breath >> out of time >> death), exterminate (to drive out).  

The "im" in immigrate is a variant of "in", which means in. You see it in words like internal (inside), insinuate (to curve in), input (that which is put in).

This "in" should not be confused with the other "in" which means "not", used in such words as indiscriminate, incapable, and insatiable. 

So, to emigrate means to exit a location. To immigrate means to come into a location.

What's the difference in meaning between "emigrate" and "immigrate"?
I'm looking for an authoritative answer here. Where does the Spoils card end up after being played twice by Counterfeit?

In fact, can Spoils be trashed at all? My understanding is that yes it can when it isn't played, e.g. in order to increase the value of Forager.
