Is immigration the same as changing nationality? If not, what's the difference?

It's different. Suppose you go to America. You don't have to be American to immigrate to the United States, but you must have a green card. If you change your nationality, you usually get a green card. So most people choose to get an American green card without changing their nationality. Because after you have a green card, you don't need a visa to go to the United States, and you don't need a visa to return to China (changing your nationality means that you are an American, not a China, and you need a visa to return to China. )