Until I started this project, I tended to get "emigrate" and "immigrate" mixed up. But no longer.
"Emigrate" means to move out of a country.
"Immigrate" means to move into a country.
The word "emigrate" came from the Latin emigrare which came from the prefix e- (a variation of ex-) which means "out of" and the migrare, "to migrate."
The word "immigrate" came from the Latin immigrare which came from the prefix in-, "into" and migrare, "to migrate."
When the Hayward family left England in 1853, they emigrated from England and immigrated to Utah. Someone who comes to the United States is an immigrant.
When Johan Wessman left Sweden in 1896, he was listed in the Swedish government's emigration records "Emigranten Populär, 1783-1951." When he arrived in New York several weeks later, he was listed in the Ellis Island immigration records.
In a genealogy program like RootsMagic, there are two possible fields for this kind of data. (Although you can always create custom fields.) The emigration field should list the date the person left his or her home country. The immigration field should list the date he or she arrived in the United States. Here is a picture of Johan Wessman's genealogical record showing the two fields.