You are right deportation is not the samething as imprisonment in a different country.
One might lead to the other anyway.
If you flee because you are political persecution in your country you might want to seek asylum and not just cross the border and hide illegally.
And when you want to claim that this was a american citizen that was deported. Then you would have an extraordinary claim with an surprisingly easy evidence on your hand. No extraordinary evidence needed just prove of citizenship.
