If two British people are talking about immigrants, they are discussing people who have moved to Britain. If two British people are talking about emigrants, they are discussing people who have left Britian. "Migrants" is a broader term which just means "someone who has moved countries" without emphasising the "from or "to" aspect. "Immigrants" and "emigrants" are both a subset of "migrants"

In Britain an immigrant is a foreign person who has come to Britain to live permanently. An emigrant would be a Brit who has gone abroad to live permanently. Although there is a verb 'immigrate' we rarely use it, but when I look at my country I often dream of emigrating. Migrants are people living abroad, usually temporarily, usually for work. If I visit my cousin in Australia for a week I am a visitor, not a migrant. A migrant worker might be somebody like a hotel worker or IT specialist working temporarily away from their home country: we would not call them emigrants or immigrants, because the move is not permanent. Many birds migrate too, spending the summer in Britain and the winter somewhere nice. Confusingly, Immigration is also used as the name of the department of an airport where people arriving from abroad get their passport checked. People passing through Immigration at an airport are usually called 'passengers', and the verb used to describe the action is 'to enter the country': some of them will be immigrants (as described above) but others will not - e.g. Brits arriving home from a holiday in Spain.

Consider three words: immigrant, emigrant, migrant. In the United States, in the 1880s, railroad companies wanted people to come and settle in the US region called the "midwest." They wanted to increase the value of land they owned.They advertised in Norway, telling farmers how good the land in Minnesota was. People left Norway, came to Minnesota, and settled there. They were migrants. They were migrating from Norway to the United States. From the point of view of Norway, these were emigrants. They were migrating out of Norway. From the point of view of the United States, these were immigrants. They were migrating into the United States. "Migrant" can be an inclusive term that includes both immigrants and emigrants. It also has the slightly different meaning of itinerant workers; for example, agricultural crops may be harvested by "migrant workers" who travel from place to place as the crops become ready to harvest. In the United States, the word "immigrant" evokes a mixture of feelings. It evokes negative feelings in people who are opposed to immigration. Therefore, sometimes the word "migrant" is used to soften the meaning and avoid those connotations. Language used by politicians is full of many examples of pairs of words and phrases that logically have the same meaning, but inspire different feelings. For example, there is a tax on inheritances of more than $10 million. Politicians who support this tax call it the "estate tax," because the word "estate" sounds dignified. Those who oppose it call it the "death tax," because the word "death" sounds unpleasant.

Amazing question

Immigrate is you are "coming into" a country migrate is much broader which is only referinf to moving. Migrate is all about changing the location while immigrate is more focused on leaving a country to go to another