The first two seek safety from violence due to political strife, civil war, or religious persecution.
A refugee has left their country, but remains stuck in refugee camps in a second country for 3-7 years or more, before the third country accepts them.
A person who seeks asylum flees their home and arrives on the shores of the new country, seeking safe haven.
An immigrant leaves by choice to better their economic circumstances, not due to threat on their safety.
As we would wish others to help us if we were in danger, let us help those of the world that are in danger right now. The citizens of Afghanistan, Bhutan, Burma, Congo, Eritrea, Iran, Iraq, Somalia, and Syria are just a few of the people that leave so that they can avoid torture, imprisonment, and death. Let America be kind and compassionate to those that need our help. We are a rich country and can afford to share our land and resources.
A few facts regarding who settled what is now the United States of America, which means your predecessors, mine, and most Americans (who have not emigrated from another country recently):
(Please note that the earliest settlers of America were the Native Americans from 5,000-10,000 years ago until Europeans invaded in the second millennium.)
1) Texas was settled by native Americans of Asiatic origin, followed by Italians, Spaniards, English, Africans, French, Swiss, Germans, Belgians, Norwegians, Prussians, Jews, Syrians, and Greeks, just to name some.
2) Some that settled Illinois were Native Americans, followed by Germans, and English.
3) Immigrants who settled Connecticut include: Native Americans, followed by Dutch, and English
4) Georgia was settled by Native Americans, followed by Spaniards, other Europeans, and then Cherokees after the initial native populace was decimated by European disease.