Emigrate and immigrate both deal with moving from one country to another, but they look at the move from a different side.
Emigrate means to leave your country to live somewhere else. The focus is on where you are coming from.
Immigrate means to enter a new country to live there. The focus is on your new destination.
It is about point of view, not only prepositions. “She emigrated to Canada” and “She immigrated from Brazil” are both correct. Seen from the country people leave, they emigrate. Seen from the country they arrive in, they immigrate.
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