Distributors for the big food companies (Coca-Cola, Pepsi/Frito-Lay, etc) essentially rent and maintain a section of shelving and then keep it full and decide themselves on the distribution of products that appear. Smaller manufacturers sell their product wholesale to the stores who then stock them in the normal fashion.

The end caps of isles are sold to the highest bidder, typically by the week; if that bidder is coca-cola they manage that display as well, subject to the constraints of the store.

One of the innovations of Frys Electronics was to try to run their shops that way, as they started by selling serial cables and other computer supplies in their family's grocery chain. It only partially worked as the vendors weren't really equipped to do this, the way the food companies are.

I believe this only applies to a few sections—soda, chips, and magazines(?). Your produce and canned food aisles are stocked by the store employees, though the planograms for the shelving layout comes from corporate, sized for the store’s footprint. There may be some distributor input into those, such as cereal, but I’ve never seen those processes, only the resulting stock plan.

This also only applies to some stores - not all. You can often tell by the uniform the sticker is wearing.

Smaller stores and chains are often stocked by the store itself, even if Coke delivered the pallet.

This is correct. In many areas, alcohol is also stocked by distributors. But the rest of the grocery store is stocked by store employees.