Dilation is a transformation of scaling that requires a center of scaling and a factor of scaling. Similarity is a relationship between two figures when there is a special transformation that transforms one figure into another. This transformation can include any combination of rotation, shift and dilation. That's why a pair of a source and its image after dilation are similar, but not all similar figures can be connected by dilation. For instance, rotation and/or shift transform a figure into another, similar one to the original, but not related through dilation..
