When an animal dies, the carcass usually lays at the surface (either subaerial or subaqueous), and may desiccate, decay, or be eaten by scavengers etc... until it is either completely obliterated, or buried. If it 'survives' to burial, then it may undergo further microbial decay etc... If it survives that, then it may become fossilised via, for example, infiltration of mineral rich groundwater into bone, and replacement of the organic fraction of the bone. All of the agents that act upon an animals remains, potentially destroying it, but sometimes preserving it, fall under the banner of taphonomy.
There are some authors who describe these taphonomic stages as pre-burial, burial, and post burial. Fairly straightforward. Or some call it pre-burial, biostratinomy and diagenesis. Or necrology, biostratinomy, and diagenesis. Or just biostratinomy and diagenesis. Or biostratinomy and fossildiagenesis.
Why can't we use the one set of standardised terminology? As a general rule, I think authors should use the terminology of their peers, or if that terminology seems defunct then propose why theirs is more suitable. But it can make for some very disjointed reading, and one cranky PhD student!