Often times history textbooks will refer to "New Immigrants" as those moving to the US between 1880 - 1920. "Old Immigrants" are those moving to the US between 1810 and 1850.
These immigrants are similar in that they mostly came to America for the same reason: economic opportunity. Some worked in or started businesses in the major cities. Others, most of them, wanted to move west into the new territory we controlled and start their own farms. Since both new and old immigrants were mostly from Europe, all the land there had been owned for hundreds of years, and ordinary peasants had no chance. Come to America, and they do.
The main difference is which part of Europe they came from, and the numbers of immigrants. There were many, many more "New Immigrants'" than old, 20 million people between 1880 - 1920. And the New Immigrants came mostly from southern and Eastern Europe, which meant they were almost all Catholics. You'll notice by 1910 there is much more anti-Catholic sentiment in the US, and that's one reason. New Immigrants included Jews for the first time too. Lastly, more of the Old Immigrants came for land than New, as many of those immigrants stayed in the cities and never moved west.