So... A sun in “traditional rasterized lighting” renders uses an orthographic camera to render the depth. Later on you calculate the depth based of the camera that renders your game (what you see) and compare the 2. Usually you do this 2 or 3 times with different sizes, that’s why sometimes you see a line where shadows become higher res in some games. (most games now a days blend them).

visual example (just look at the pictures): https://learnopengl.com/Advanced-Lighting/Shadows/Shadow-Mapping

For small lights (lamp not a sun) you draw light volumes and use all the other data (texture, normal, roughness, etc) and composite the final image with light volumes affecting the final render. (Deferred rendering, if it was forward you render the whole thing again per light). Visualize a render of only the base textures, how shiny objects are, are they metallic... All those renders are then combined into 1, the final render you see.

example: https://learnopengl.com/Advanced-Lighting/Deferred-Shading

Global illumination is basically indirect light or bounce light, most commonly, games bake this data and have some objects that can dynamically (usually characters) read the data from the positions. (Think of a huge grid with data of the average light condition in that area) An example is a white table against a red wall. If you shine a bright light against the wall, red light should bounce off on the table.

Unity explains it well: https://docs.unity3d.com/560/Documentation/Manual/GIIntro.html

You don’t see the player’s shadow because not every light can render shadows, the game would be too hard to run. You also don’t see it in the bake of GI since it is dynamic. If i shoot him and he dies... there should not be a shadow on the wall.

Sophisticated lighting simulation = raytracing. Games lie and uses hacks that are cheap in order to let you do it 60 per second. But then RTX came... so now we swap 1 hack with a “sophisticated lighting simulation”, and upscale the result (kind of like dlss / denoising) because it is still super expensive to do X amount of times / second.