It is important to distinguish a data format from a data model. The later is the convention used to store information so that a program can access the information. A data format defines only the form of the information, not the operations that can be performed on it. In contrast, a data model often does not define a particular format. For example, an integer data type (which includes properties of the object like its range and the operations which can be applied to it) does not specify exactly how such an object will be stored in a computer. It is possible to build (in software) many different implementations of a given data model which have a high degree of interoperability but which all use different internal representations.
Many data formats imply a particular data model or set of data models. Thus it is possible to translate information stored in one format to another when the two formats share data models. However, the problems that plague many APIs (lack of formalism, ...) are worse for data formats because the set of operations, rather than being at least partially defined, is purely conventional. Thus features of a particular format which may be in fact consequences of a particular implementation often must be accounted for in the definitions of the operations. Lossless translations between data formats are very hard even in limited cases and, as with APIs, impossible in general.