The smoothing ("orsatura") of the old terracotta floors has always been made by rubbing with a tougher brick or stone called "bear" ("orso").
This method left the floor looking wavy and with an undulating effect in backlit.
Today there are no more workers willing to do this heavy work.
A compromise is smoothing every tile before laying. The non-perfect alignment of the screed and the imperfections in laying allow to obtain an undulating effect of the entire surface.
The stamps which appear are removed with a light dry sandpapering. A deep-water smoothing of the surface would risult in a mirror effect, altering completely the aesthetics of the floor.