So I have been wanting to make a rendering engine as a summer project. I'd like to shoot for photo-realism of static scenes rather than real time dynamic game like graphics. So in my research I came across two major techniques for going about this. One is to attempt to directly solve the rendering equation with specialized numeric methods like bidirectional path tracing. Another is the well known ray tracing technique. Ray tracing is a) much simpler and b) more efficient. Additionally it seems as though some kind of interpolation/de-noising is needed to make the images look properly smooth when path tracing techniques are used.
I understand recursive ray tracing to be an algorithm in which rays are shot out from the eye and collide with objects in the space. When they do more rays are shot from that point to calculate the lighting at that point.
I understand path tracing to be trying to find paths to the viewing plane from light sources. If enough of these paths are sampled without bias then you can use these paths to perform monte carlo integration over the space using the found paths as your sample points.
What effects are captured by path tracing that are not captured by ray tracing