All transformations are functions, but it would be wrong to describe most functions as transformations. Typically a transformation operates on a space or other mathematical structure, and preserves at least some of the structure's features. Often (but my no means always) the result of the transformation resides in the original space, or at least in a similar kind of space. Both "transformation" and "function" are nouns, so no grammatical error is committed when substituting one for the other.
(Added) As an example, consider the positive real numbers as a "space", with the logarithmic transformation (any base you like). When a product is transformed, it becomes a sum in the transformed space, which is the whole real line. Structural features of multiplication, such as associativity, commutativity, and continuity, carry over to the corresponding addition. Of course, the logarithm here is a function as well.