A great deal—even though the terms are often used interchangeably.
But the distinction becomes important because the world is witnessing the worst refugee crisis since World War II—one with sometimes-tragic consequences. Here’s how the United Nations High Commissioner for Refugees defines refugees:
Refugees are persons fleeing armed conflict or persecution. … Their situation is often so perilous and intolerable that they cross national borders to seek safety in nearby countries, and thus become internationally recognized as “refugees” with access to assistance from States, UNHCR, and other organizations. They are so recognized precisely because it is too dangerous for them to return home, and they need sanctuary elsewhere. These are people for whom denial of asylum has potentially deadly consequences.
Migrants, on the other hand, “choose to move not because of a direct threat of persecution or death, but mainly to improve their lives by finding work, or in some cases for education, family reunion, or other reasons.” The UN agency continues:
Unlike refugees who cannot safely return home, migrants face no such impediment to return. If they choose to return home, they will continue to receive the protection of their government.
Countries grant refugees certain protections under their international treaty obligations. This is why some states are reluctant to grant those people who are fleeing unrest in their home countries refugee status. Here’s more from the UN agency:
Politics has a way of intervening in such debates. Conflating refugees and migrants can have serious consequences for the lives and safety of refugees. Blurring the two terms takes attention away from the specific legal protections refugees require. It can undermine public support for refugees and the institution of asylum at a time when more refugees need such protection than ever before.
But who you are can sometimes dictate how you are perceived. Here’s Karl Sharro, a London-based satirist and architect: