The words emigrate and immigrate are both verbs that sound similar, but they're antonyms. That said, both words are concerned with living and where people intend to do their living.
So let's look at the differences between emigrate and immigrate and when to use each.
Emigrate vs. Immigrate
Emigrate is a verb that means to leave where one lives (especially in relation to a country) to live elsewhere. As such, emigration is the process of leaving a country with the intention of living somewhere else moving forward, and the people who leave a country for such a purpose would be called emigrants.
Immigrate is a verb that means to enter a country of which one is not a native with the purpose of setting up permanent residence. As such, immigration is the process of entering a non-native country with the intention of settling in the non-native country, and the people who do this are called immigrants.
Here are a few examples of emigrate and immigrate:
Correct: Joey was offered a better job in Belgium, so he's deciding whether to emigrate from the United States to take it.
Incorrect: Joey was offered a better job in Belgium, so he's deciding whether to immigrate from the United States to take it.
Correct: Many of my ancestors decided to immigrate to North America around four centuries ago.
Incorrect: Many of my ancestors decided to emigrate to North America around four centuries ago.
Correct: After they married, the couple decided to emigrate from Australia and to immigrate to Canada.
As the final example shows, a person can simultaneously be an emigrant and immigrant. They can also emigrate at the same time that they immigrate. It's all a matter of geographical perspective.
Here's how I keep it straight in my head: The "e" in emigrate is the same as the "e" in the word exit, as in exiting a country. Meanwhile, the "i" in immigrate is the same as the "i" in the word in, as in to come in to a country.
No matter what type of writing you do, mastering the fundamentals of grammar and mechanics is an important first step to having a successful writing career.