Is there a difference between transform and transformation? I was told that there is a difference between a transform and a transformation. Can anyone point out clearly? 
For example, is Laplace transform not a transformation?

This is a solidly common-usage question, which I was asked many decades ago, and has now come up again.
In common usage, when referring to the alteration of elements of a set, as an abstraction, (or as Niall says, a "process"), the word transformation is always applied.  The set is transformed, action is a transformation.
When referring to the transformation itself as an object, as a thing that performs the transformation, the word transform is often applied.  (This includes the "named" transformations that Ooker refers to.)  But clearly, there is a direct correspondence here between the action and the actor --- it could be viewed as a matter of emphasis.
But the terminology isn't cut-and-dried at all.
P.S. The terms operator and transform are usually restricted to mappings whose range and domain are homomorphic.  These are used in very much the same way, except, I don't think I've ever seen transform applied to mappings of finite-dimensional spaces.
