Ray tracing is a more generic term that covers rendering techniques which trace rays between a camera and a scene. Back in the day everyone used Whitted style ray tracers to render shiny metal blobs because secular reflections are trivially handled with ray tracing. Unfortunately other physical aspects of light like diffuse reflections were not handled by early ray tracing algorithms.

Kajiya introduced the rendering equation, a mathematical formulation of global illumination (takes diffuse, secular into account). It's a multidimensional integral equation. Unidirectional path tracing is an algorithm he introduced to solve the rendering equation. It uses several rays traced from pixels in the camera bouncing randomly through the scene. It's a Monte Carlo integration algorithm for solving the nasty integrals.

Photon mapping involves a pass algorithm tracing light from light sources into the scene, then a pass (like path tracing) gathering that light back at the camera. It better handles more complex light effects like caustics.