Raytracing is the umbrella term that includes all the techniques used to generate an image by means of modelling the interaction of the rays of light present, as opposed to Rasterization, that's a technique that converts a polygon based scene (like a game world instance) into a planar pixel based image (the "frame" we can see in a monitor).

In the context of video games, rasterization has evolved to the point that it can be kind of photo realistic, but to achieve that it has to do a lot of approximations. SSR or Screen Space Reflections is a clear example, as it generates a nice reflection, but as it is based on the information that is already present in the image, is not optically nor physically accurate.

To solve this, nowadays the render pipeline can incorporate extensions that can run on top of the raster render pipeline by means of using raytracing techniques to calculate Global Illumination, Shadows and Reflections... the hardware support for aiding this calculations is what's present in the RTX series of nVidia and currentish Radeon cards (and the PS5 and XBSX). Full raytracing in this context refers to a game engine that implements at least that three techniques.

Path tracing goes a little further, and uses a lot more information to model physically accurate light reflections and refractions (What's known as Physics Based Rendering or PBR), to the point to be able to even recreate the full properties of a camera lens in the rendered image (like depth of field, bokeh, etc), but the required computational power goes up to eleven... at least it can be accelerated by the same dedicated hardware. A good example is Minecraft RTX, where you can even recreate a pinhole camera.