Vellum is parchment made from calf skin. The National Archives site gives a brief and clear account. Whether vellum parchment was/is particularly smooth or not I’m not sure, but we now use it as a descriptor of a paper sheet that is smooth but not too smooth. In the crafts area, vellum refers to a translucent paper.

According to Wikipedia UK Acts of Parliament are still printed on vellum. I wonder if this is still true. Their reference is to a BBC article from 1999 telling how Parliament had just rejected a change to paper only.

(See also Parchment)