Hi Jose Rocha,
I am neither a teacher nor a native English speaker. Here are my two cents. Hope this hopes.
1) emigration is from the standpoint of the native country from which people move out.
(You are an emigrant for the native country)
2) immigration is from the standpoint of the adopted country which people move in.
(You are an immigrant for the adopted country)
eg1. I am a Chinese citizen. If I moved from China to the UK permanently, I were an emigrant for China.
eg2 I am a Chinese citizen. If I moved out from China and settled down in the UK permanently, I were an immigrant for the UK.
The prefix "e" means move out and the prefix " im" means move in.