Are the NIE and the NIF the same thing ?

Yes and no.

The  Numero de Identificación Fiscal (“NIF”), must be applied for at the Tax Office, and the number would be the same than the NIE, which is released by the Police. So NIE and NIF are different things (because they are released by different authorities and for different purposes) but  actually have the same digits. In short, by knowing your NIE you already know what would be your NIF, but this does not mean that you have a NIF until the Tax Office assigns it to you. Actually, most people uses both numbers as synonyms.