Looking at the differences between the various telegraphic facsimile devices, most interesting to me are devices that simultaneously create a document in two locations, by a person writing, doodling, etc. in the transmitting location and elsewhere by the receiving instrument which is executing the exact same movements.
This method, most prominently applied by Elisha Gray's telautograph of 1888/1893, is very different from devices that read an existing document and reproduce it at the receiving station.

Watching the receiving instrument of the telautograph producing an absent person's handwriting must have been a curious experience. A source in 1904 described it this way:

There is something distinctly weird and creepy in the sight to the onlooker who watches this pen gliding, without human touch, over the sheet, while a well-known handwriting stands out, word after word, in its swift, silent track.
A sum is set down, figure by figure, and worked out, a sketch made, in the same wonderful way. Then the pen stops, the bell rings twice, and the message is done, and the paper rolls itself in place ready for the next call...

Priscilla Leonard, "Writing By Wire." The Youth's Companion Sep 29, 1904. 453.

Gray himself claimed that

[the telautograph] is the most flexible of all means of communicating at a distance. More so than the telegraph or telephone, because these can only communicate words, while the telautograph can convey ideas by diagram, drawing or any form of hieroglyphic. More than this, it will transmit in a measure the individuality of the man himself.

Elisha Gray, "A Revolution in Means of Communication." The Cosmopolitan May 1893. 127.

The example in Gray's article actually includes, besides handwritten text and numbers, of course, a drawing of a flower. I might just set out to find examples of reasonably private transmissions (as opposed to business/banking where the telautograph predominantly was used) for my thesis.