I just want to make it clear to me if there is a difference between 'smoothing' and 'smoothening' or if one of them is incorrect. 'Smoothing' is used far more often according to Google search, but occasionally I see the other version too. I found identical definitions for them both but they seem to derive from different verbs. I suppose the actual question is, what is the difference between 'smooth' and 'smoothen', but I am looking for a noun to use when talking of the act of making something smooth.
You make things smooth - you smoothe or smoothen them (and while these were appearing in different proportions in the past, they have nearly evened out nowadays).
The activity though is called smoothing (a surface) or smoothing out (faults, creases, folds, whatever disturbs the surface).
smoothening is definitely not a term in common use.