Frameworks for Classical Mechanics

There are three frameworks used for describing classical mechanics called Newtonian mechanics, Lagrangian mechanics and Hamiltonian mechanics. All are equivalent in the sense that they yield the same results and describe the same phenomena but they differ in the way they reach said results. It is important to remember that these frameworks are just formulations and neither is more or least correct than another. They are like different languages - they all describe the same thing but using different words and grammar.