The Consumption Item descibes the consumption of a service like a phone call. The properties contain all data characterizing the service consumption. This includes references to parties like the business partner and so on. A consumption item can only have the status "raw", "raw excepted", "unrated", "unrated excepted" and "rated".
The Billable Item descibes an amount that is charged to a certain contract account (which in turn belongs to a customer). A billable Item can result from one consumption item or one rating item or several rating items - depending on the setup. Its status can vary between "raw", "raw excepted", "billable", "billable excepted", "billed" and "invoiced".
A rating item describes an aggregation of usually several Consumption Items for the sake of data reduction. Such an aggregation must be supported by the business logic of course. Rating items do not necessarily have to be persisted on the database. They can be records only created as an intermediate object.
The fundamental differences between the BRIM data model and the TMF data model are from my perspective: