Tests written against an implementation rely on internals of the code which are not part of the interface. As a very simple example, say you have a module which takes input A and B, merges that data into a data structure C, then performs some calculations on it and gives you back D. If you were testing against the interface(black-box), you'd write tests which put in A and B and check whether you get the correct D out. If you were to write a test against the implementation(white-box), you'd also check whether C conforms to your expectations or whether the algorithm to turn C into D works a particular way. If later the module writer decides to change the implementation and do without the intermediate C (or change it in some way), the test breaks.
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