You partly answered the question yourself.
In Australia, you can have a distinctive ring pattern to distinguish incoming Fax calls from voice calls. If there is no DR, then the Fax machines have to recognise each other.
The Fax machine at the sending end sends bursts of tone and waits for a response. If the call is answered by a Fax machine it responds and they exchange data to determine the speed and format that the machines can use (one may be less capable than the other, so they must communicate at the lower level).
I don't know how computer to computer communication would work, I assume it would be similar.