I think it's clearer to see the distinction between an information model and a storage model: The fundamental goal of an information model is to provide a mechanism to convert input information into output information. But if the model is so degenerate that it just echos back the same data in the same format that was put in (at a different time), then it's probably better to call it a storage model.
The relational model is a logic system that lets us use predicate calculus to infer from one set of propositions taken to be true, a second set which is by implication true. That is, it provides a means to obtain encoded answers in response to encoded questions applied to a body of encoded facts.
And a KV store is clearly a storage model.
And there are some in-between, such as the CouchDB document store, that can transform one body of information to another, but also pay attention to physical storage issues.