I'd define classical physics as any physics which is not quantum, i.e., an approximation whose validity is constrained by the quantum nature of all Natural Laws.
General Relativity is the most complete theory describing all phenomena within this validity domain of classical physics. Special relativity is the approximation where all gravitational effects can be neglected, and Newtonian physics describes systems where gravity is only very weak and all velocities are much smaller than the universal speed of relativistic physics (which is with very high accuracy identical with the phase velocity of electromagnetic waves in the vacuum).