This distinction is very clear and has really never been a problem for people who understand language. The English Wikipedia has somehow managed to fuck it up beyond all recognition, so congratulations! You're one of Today's Lucky 10,000!
I prefer 'migrated' for exactly that reason - strips all the annoying modifying prefixes that can trip you up. More flexible word, less radicals! ;)
It's funny to me people are only discovering this about America now whereas a whole generation of 1st gen parents of current Americans discovered it in earlier waves, the tech waves, etc.
Sorry for correcting grammar. But being from one of the previous colonies, one desires to be a master of English and help others also to master it.
We emigrate to a country from our own country.
And other people immigrate into our country from some outside country.