I don't believe there are absolutes with these definitions because many authors fall into more than one category, but I will try to simplify it for you. Native Latino literature usually refers to literature written by Latinos that are living in their native countries. They write in their native language and the works are translated into other languages. Examples of native writers would be Gabriel García Márquez, Federico García Lorca, Octavio Paz, etc. Márquez, however, could be considered a cross-over because he tried to seek asylum in the U.S. but because of his ties with Castro, was denied. He lived abroad for awhile, but returned to Cuba.
The literature of exile, or sometimes called diasporic literature, is written by Hispanic authors that are in exile from their countries -- many Chilean writers, for example, such as Isabel Allende, who lives and writes in California. Ricardo Eliezer Neftalí Reyes y Basoalto (aka Pablo Neruda) also was a Chilean writer that was forced to leave Chile and wrote from exile for many years (from Argentina). He eventually returned to Chile. José Julián Martí is a Cuban writer in exile whose themes include the concepts of freedom, liberty, and democracy. Many Latino writers in exile also write about these themes, but not all.
There are many so-called Latino writers - those that write about Latino themes - that live in other countries. The U.S. has many. Sandra Cisneros and Julia Alvarez are Latina writers that write about the lives of immigrants and the struggles they have blending into American culture. Cisneros is an American, but she and her family migrated back and forth to Mexico when she was young. Alvarez, however, is a Dominican writer who was born and lived in the Dominican Republic as a child, but was forced to leave because of her father's political views, so she was a young exile, but still writes about Latino themes even though she lives in the U.S. José Antonio Villarreal is a Latino writer, but he also is American. He writes about themes of immigration and assimilation, however. Rudolfo Alfonso Anaya is also an American who is considered a Latino writer. You can see how these categories are interconnected.