Immigration is the act of moving into a country of which you are not native-born. In contrast, emigration is the act of moving out of a country. A person moving into another country is called an immigrant, while an individual moving out of a country is called an immigrant. A lot of factors are responsible for the movement of people from one country to another.
Most times, people leave their country for another country in search of a better life, better opportunities. At times, people travel out of their country to seek asylum in another country due to issues like war, conflict, political persecution. Although immigration and emigration are two different terms, they can still be used for someone traveling from one country to another.
For instance, a person moving out of my country will be called an immigrant, whereas the same person will be called an immigrant in another country.