In a comment to the top answer of [this][1]  question Darij Grinberg says that 

> the problem with the dynamical perspective is that it is way harder to
> grasp for algebraic/combinatorial-minded people than any formula,
> however complicated it is. I still don't get the difference between a
> transformation of points and a transformation of coordinates; for me,
> they're all endomorphisms of a vector space.



Since apparently I'm also an algebraic minded person - I neither can see a difference between those transformations and also view only as endomorphisms - I would very much like to know what their difference consists of (even if the difference manifests itself only on the level of intuition and not of formal mathematics).


  [1]: https://mathoverflow.net/questions/7584/what-are-the-most-misleading-alternate-definitions-in-taught-mathematics/7952