Calligraphy vs. typography?

After reading an extract by Beatrice Warde ("The Crystal Goblet"/"Printing Should Be Invisible"), it got me thinking about how calligraphy and typography differ. To be honest, I had always 'grouped' the two together in a sense, but Warde made the point that "Calligraphy can almost be considered a fine art nowadays, because its primary economic and educational purpose has been taken away". The fine arts allow for the individual's experience of the art to be unimpeded by their reasoning faculties, and to simply rely on their aesthetic ones. The purpose of printing, however, is not purely aesthetic at all - but is to engage with the reasoning faculties of the reader.

As Warde points out; "Type well used is invisible type" - which reminds me of the phrase "form follows function" (relating to 20th century design). Type serves the primary aim of 'doing something', whereas calligraphy can be considered to be more of a fine art, and thus is more interested in existing as "an expression of beauty" instead.