The distinction is important because there is no necessary connection between burying the dead and any coherent notion of an afterlife. To take only the closest example, I don't believe in an afterlife but I would still be troubled by the sight of hyenas tearing into a relative's corpse. Elephants sometimes put considerable effort into hiding their dead. I think that both burial ritual and conceptions of an afterlife are rooted, separately, in the feelings stirred in us by death. When we bury the dead we are expressing primarily emotions and only secondarily (if at all) theology.
The Neanderthals were found covered together with rocks burying their remains. The researchers believe it's likely that other Neanderthals intentionally placed the rocks over the bodies from a height. While it cannot be ruled out that an accident killed the three individuals, the scientists believe that wasn't the case.
"I think there is just enough evidence at Sima de las Palomas to think that three articulated skeletons are unlikely to have been the result of a single random accident to three cadavers that somehow escaped the ravages of hyenas and leopards, which were present at the site," Walker said.
Unburnt bones of two articulated panther paws were embedded in rock "in an area where the rest of the animal's skeleton was conspicuous by its absence notwithstanding its proximity to the human skeletons," the authors write.
The researchers speculate that a Neanderthal cut off the panther paws and kept them. It is also possible that the paws were added to the bodies before burial, perhaps holding some ritual significance.
It is all too common for people to see a pile of valuable goods in a grave and think, "Look, these people believed in an afterlife where the dead could use pots, swords, and gold!" I doubt it. By placing valuable objects in the grave people were giving expression to the emotions of loss, to a felt need to sacrifice, to their own aspirations for status -- funerals were in many societies a major site for competitive display -- and perhaps to feeling creeped out by having the deceased's most personal belongings still lying around the house. None of this presupposes a theology of an afterlife as a world like this one.
The relationship between ritual and belief is complex, and when they agree point by point it is just as likely that the theology has been articulated to explain the ritual as that the ritual is an enactment of the theology. Emotion is prior to either, and since all higher mammals (at least) experience strong emotion, there is no necessary connection between giving expression to emotion and any sort of higher, human thinking.