The main difference among both is that Classical Mechanics are all rigorously observed under the Laws of Motion of Newton, also known as the Three Laws of Mechanics; whereas the Quantum Mechanics do not observe these Laws in a fullfilling manner. For instance, the Three Laws of Motion stipulate that an object that switches behavior from rest to motion undergoes a transitional stage known as acceleration; it has been observed that when a quantum or photon is emmited by an electron, it doesn't undergo said transitional stage, but it is rather thrusted all the way into light speed. The Classical Mechanics work for objects that are primarily made of matter, while the Quantum Mechanics work for objects that can hardly be called objects, for they are primarily made of energy, or carry few or no matter at all.