Hi Kate,
This is a great question. It varies by the artist, but I would say the majority of calligraphers that do invitations prepare a “camera ready” image that can be used to have the invitations printed. It is rare, but not unheard of, that someone would hand calligraph every single invitation. Usually the calligrapher prepares an original which is then digitized so a digital file can be sent to the printer or bride.
When I did invitations, I did the whole process, specified papers, had the invitations printed (either letterpress, thermography, or engraved), etc. and send the finished pieces to the bride. This was a lot of work and very expensive but I catered to a high end client.
Many wedding calligraphers only calligraph the envelopes (provided by the bride) and/or the place cards for the reception.
I hope that helps! Let us know if it prompts more questions.