In this paper we recall some of the essential properties of the classical Darboux transformation and establish its equivalence with the dressing method. In this way we can elucidate and co-ordinate different notions existing in the literature, like Darboux matrix, Darboux transformation and Backlund transformation, which, although being different, are nevertheless related to one another. As an example we are then able to construct a strict analogue of the classical Darboux transformation for the Zakharov-Shabath-AKNS spectral problem.