Where and how do you draw the distinction?

Good question. I doubt if those ancients had a concept of religion. They were just following social customs.

Perhaps a combination of both plus a third factor that may well have been the origin of all burial practices that no one has mentioned. Completely nomadic groups that were constantly on the move in the African savanna could leave their dead where they fell without consequence. Later groups settling in certain locations for some time (cave dwellers is one example) faced a problem when it came to their dead. Aside from the disagreeable odor of a decomposing body in the house there was the existential problem of the scent attracting predators and large scavengers.

I am of the opinion, based on what evidence there is so far, that burial was originally driven because of survival/odor issues and that any ceremony revolving around the burial of clan members came at a later stage. Of course I could be wrong, but it seems to be the more logical sequence.