Quantum mechanics is the current name of the field of quantum physics. In quantum mechanics, physicists study how atoms, the components of atoms, and other tiny particles behave. These are called “quantum particles” and include electrons, protons, photons, and so on. They follow the laws of quantum mechanics.
In the early 1900’s, physicists, through experiments, discovered that atoms and their components followed different laws from those of ordinary objects like tables and chairs. The mathematical laws governing the movements and forces among ordinary objects is known as “classical mechanics” or “Newtonian mechanics.” For example, Force = Mass times Acceleration is a mathematical law of classical mechanics.
Drawing of a photon (in green) being emitted from carbon molecules. [Image source: Nancy Ambrosiano, Los Alamos National Laboratory, July 2017 News Release, “Single-photon emitter has promise for quantum info-processing,” (Public domain)]
When physicists realized that quantum particles do not follow the laws of classical mechanics, they called the new field “quantum theory.” At first, physicists developed quantum laws which were heavily verbal, rather than highly mathematical.
In the 1920’s, physicists developed mathematical laws which describe quantum behavior. In particular, Erwin Schrodinger and Werner Heisenberg developed the key mathematical laws governing quantum particles (Schrodinger’s Wave Equation and Heisenberg Matrix Mechanics). At this point, physicists began calling the new field “quantum mechanics” on the model of the phrase “classical mechanics.”
The term “quantum mechanics” means the same thing as “quantum physics” though the term “mechanics” emphasizes doing calculations.