We reveal the classical and quantum regimes of free electron interaction with radiation, common to the general variety of radiation sources (e.g., a Smith-Purcell radiation), the dielectric laser accelerator, and photo-induced near-field electron microscopy (PINEM). Modeling the electron with initial conditions of a coherent quantum electron wave packet, its topology in phase space uniquely defines a universal distinction of three interaction regimes: point-particle-like acceleration, a quantum wave function (PINEM), and a newly reported regime of anomalous PINEM (APINEM). The quantum interference beat of APINEM is capable of improving the spectral resolution of postselective electron microscopy. The particle-wave duality transition between regimes reveals the history-dependent nature of quantum electron interaction with light.