Classical vs Quantum Hall Effect
The Hall Effect was observed and explained by Edwin Hall about 130 years ago as you say. This is the 'classical' phenomenen that is easily explicable and can be demonstrated with modern school or even home equipment if you're a techie.
The Quantum Hall Effect was predicted in the 1970's and not observed until a few years later. It is much more difficult to explain and observe. It's actually a 'quantum aspect' of the Hall Effect.