Terror Birds were a family of large predatory birds that evolved in South America but also migrated to North America. The birds that Andy met were most likely Phorusrhacos. They were similar to, but not directly related to the Gastornis.
2.5 million years ago in South America, Terror Birds preyed upon Macrauchenia and they were in direct competition to the North American sabre-toothed Smilodon. One time, three Terror Birds stole Andy's Gizmo and took pictures of themselves before Andy chased them away. (APA: Sabre-Toothed Cat and Roar)