The Calligraphy skill is defined as “a formal stylized handwriting” (BWG, p. 263), so on the face of it seems like an ability to physically write (rather than compose) a letter. And the root of the skill is averaged with Agility, which suggests “doing” rather than just “thinking”.
However, the tool requirement for Calligraphy is not Expendable, which strongly implies it doesn’t require ink, quills, sopping sand, or other things that are subject to exhaustion or wear; i.e. that the tool kit is reference materials of which version of an illuminated X is best for this situation, special rulers, proforma documents, &c.
This contrasts with the Write skill which is stated to have an Expendable tool kit, so requires ink or their ingredients (and is defined as “a copyist’s skill” (p. 309) so is explicitly the ability to physically write).
Obviously, they can FoRK into each other when creating a formal letter, and a character who has Write but not Calligraphy can’t create a new letter in formal handwriting (without using Beginner’s Luck) and—almost certainly—faces higher Obstacles if trying to copy an existing letter in formal handwriting if they are allowed to try at all.
But, what can a character with only Calligraphy do?
Are they limited (as is suggested by the tools not including expendable items) recognizing messages in the choice of illumination, assessing whether the letter was altered or faked, and other “knowledge” of the formal writing style—and thus the root including Agility is an oddity.
Or are they able to physically write (as is suggested by the Agility half of the root) as well—and the enduring nature of the tools is an oddity.
While it seemed merely an interesting niggle when I first noticed it, if Calligraphy does include the ability to write but does not expend tools to do so, it would allow characters to make a fortune by spending their free time creating copies of books (which seems somewhat contrary to the BW ethos of everything of value costs the character something meaningful).