Well I can explain GI and FG and Caustics to you, like what they do-

Gi is the amount of initial photons cast out from the light. These photons are bounced around, adding color, and stored for later use.

Then FG comes in, looks at the photon map, what the above did, and shoots more photons (fg rays) from each gi point. That is then approximatied, and the img is made.

Caustics are done the same way as GI, except that the photons are shot out, and if they dont hit a reflective or refractive object they are ignored. If they do, they are traced to the point where they hit another objcet, stored in a photon map, and then the FG comes out and approximates them.