If a refugee is someone “pushed” from his or her native land, and an immigrant is one “pulled” to a new country, then the vast majority of the tens of millions of people seeking to move from the poor global South to the rich North belong to both categories.

The tens of thousands of youthful border-crossers who claimed asylum in the United States in the summer of 2014 were described by supporters as refugees from gang violence at home in Central America. Yet 2014 was a year in which gang violence dramatically abated in Honduras and Guatemala. The “push” was stronger two years earlier ... but the surge responded to the “pull” of perceived opportunity.

Even with the Syrian refugees, “pull” matters as much as “push.” Most of the Syrians en route to Europe are immediately fleeing—not the dictator Assad’s barrel bombs—but the tedium and futility of Turkish refugee camps. When European border controls collapsed in the fall of 2015, Syrians and those claiming to be Syrian rushed, not to any European country at random, but very specifically to the countries with the strongest job opportunities and most generous welfare systems: Germany and Scandinavia. Every day, at the entrance to the Channel Tunnel, young men described as “refugees” risk their lives to reach Britain from ... France.

The distinction between migration and asylum-seeking is grounded less in differences of motive, and more in an artifact of international law. Shamed by the exclusion of German and Austrian Jews in the 1930s, the post-World War II democracies signed treaties and conventions that conferred rights of asylum on persecuted people. If a person who wishes to resettle in one country can gain recognition as an asylum-seeker, he cannot easily be removed. Virtually all of the 51,000 Central Americans who jumped the border in 2014 still remain in the United States. The tens of thousands of Mediterranean crossers who falsely claimed to be refugees when they disembarked in Italy likewise mostly remain in Europe.

The immigration debate is defined by legal categories: migrant versus refugee; illegal versus legal. Those legal categories are subordinated, however, to a central political division: migrants who are chosen by the receiving country versus those who choose themselves. That political division in turn is connected to a fateful economic division: migrants who arrive with the skills and attitudes necessary to success in a modern advanced economy versus those who don’t.

Those divides are highlighted by a massive new study by the National Academy of Sciences of the acculturation of new immigrants to the United States: “The Integration of Immigrants into American Society.” The first reports on the study in October headlined comforting news: recent immigrants to the United States were assimilating rapidly—arguably more rapidly than their predecessors of the pre-1913 Great Migration. One must read deeper into the report to encounter the worrying question: Assimilate to what? Like the country receiving them, immigrants to the United States are cleaved by class. Approximately one quarter of immigrants arrive with high formal educational qualifications: a college degree or more. Their record and that of their children is one of outstanding assimilation to the new American meritocratic elite, in many ways outperforming the native-born. (The highest outcomes are recorded for immigrants from India: 83 percent of male immigrants from India arrive with a college degree or higher.) College-educated immigrants are more likely to be employed than natives, and their children are more likely to complete a college degree in their turn. Here is a mighty contribution to the future wealth and power of the United States.