it depends on your definition of 'case'. Equating 'case' with the grammatical markers used to indicate case makes for some strange combinations.
Most linguists these days go for a bit of both: overt grammatical markings (the surface morphology of case) and the function (the syntax of words and the function of case.
In Latin, for example, in first declension genitive and dative singular are the same case and in second declension dative and ablative singular are the same case.
That's not how the Romans or today's grammarians would have analysed it. They distinguished case from case-endings (or other kinds of overt markers). Even the Indian grammarians of Sanskrit, who came from an entirely different tradition, separated case-endings from case. They also divided the cases into a myriad of functions, e.g., the genitive of possession and the partitive genitive. While the names given to cases are essentially arbitrary--in fact, the Sanskrit grammarians just numbered their cases, first through seventh--they are convenient tags to discuss the various phenomena of case.
