The main difference between bilingual education classes and English as a second language, or ESL, classes is that the teacher will only speak in English during ESL classes, but can speak in both English and the native language in bilingual classes. Both forms of classes can be used to learn English in addition to a first language.
The reason for the difference in the two types of classes is the background of the students. In ESL classes, students often come from multiple backgrounds and don't speak the same first language. In bilingual classes, students typically all speak the same language originally, which allows the teacher to use it as well during lessons.