This is the immigration court. It is overseen by the U.S. Department of Justice. Immigration Judges work for EOIR in the court.
Like ICE, the CBP enforces immigration laws, but mostly works within 100 miles of the U.S. border, including shorelines and at ports of entry, like airports. Their main job is to make sure people do not enter the U.S. who do not have permission to do so.
This is the immigration office. It is overseen by the U.S. Department of Homeland Security and they handle certain immigration applications.
This is what people refer to as “la migra”. ICE enforces immigration laws and detains people who are undocumented. ICE looks for people who have orders of removal, and carries out operations to try to find undocumented people. ICE also employs attorneys who work in immigration court to argue that people should not get to stay in the U.S. ICE is overseen by the U.S. Department of Homeland Security.