To be technical, "accusative" etc. are cases (i.e. forms of words) while "direct/indirect object" are grammatical roles - those are different categories. In German, for example, the Dative case can mark an indirect object (although some verbs may require the Genitive case for its indirect object), but it can also have other functions. This is even more pronounced in e.g. Latin where the different cases can have a wide range of different functions, not just direct/indirect object.

This is possibly not something that is taught very explicitly in school, but it's what the terminology means. (Or at least it's how I was taught. Linguistics being such an old discipline used to analyse so many different languages means that different people will use terminology differently.)