Emigrate means to leave a place, such as a country of origin, to settle in another location. To immigrate is to settle in a country where you were not born.

Same as between import and export. "Im" indicates that something here came from the outside, and "ex" means that something is leaving here. So, an immigrant is a person who came from another country, and an emigrant is a person who is leaving (or have left) the country.

We usually use the noun forms, and ‘immigrant’ is more common. I’m an immigrant to Canada from Iran. Or, more naturally, I’m an immigrant from Iran. (If you’re in Canada when you say it, it’s not necessary to specify where you immigrated to. It would be understood.) ‘I’m an emigrant from Iran. ‘ is correct but a rarer thing to say. It perhaps suggest that maybe you haven’t decided where to settle yet or emphasizes that where you’ve decided to settle isn’t important in the discussion. My parents are immigrants. They emigrated from Taiwan in the ‘50s. (It would be understood that they immigrated to the country I am in)