It is an unfortunately common mistake to use these terms interchangeably but they do not mean the same thing. Only guide dogs that were trained at the Seeing Eye facility in New Jersey can properly be called "Seeing Eye" dogs. It's like a brand name. There are vehicles and there are Fords. All Fords are vehicles, but not all vehicles are Fords.
The Seeing Eye is the oldest guide dog training school still in operation in the world. It is the most famous and the most recognized and this is probably why people get confused.