Explain some of the different names used?

In the UK you will often hear the term "polished plaster" used, although this really only describes half of the many finishes available.

Venetian plaster (or "Stucco Veneziano", in Italian) incorporates all the Italian wall finishes.

Marmorino's literal translation is "little marble" and is best described as polished plaster.

Stucco is generally accepted as the term for the rough textured plasters.