I guess the common term today is FoIP (for fax over IP), but "common" may be inaccurate as it doesn't seem to be widely used. Officially, it's known as ITU Recommendation T.38. Wikipedia has a very readable article about it
here.
I'm sure you've heard the term "voice compression" if you've hung out with us weirdo voice guys for any length of time. The idea is to either 1) save bandwidth or 2) put more voice traffic through the same size pipe. It's accomplished by removing some number of sampled bits in the speech, and then process the remaining bits through any number of algorithms to "smooth it out" or clean it up. Many people's ears can't detect a lightly compressed voice call, but nearly every algorithm introduces some artifact or character that a good ear can pick up. Note that a true toll quality phone call requires 64kb/s (that's 64 x 1000 in the phone world, not 64 x 1024 as in the computer world).
Do some compresses or VoIP calls "sound" toll quality? Absolutely. You might want to read about perceived quality and MOS scoring along those lines. But here's the thing, while a human ear/brain can tolerate a couple of missing bits in a phone calls, machines like modems and faxes cannot because each and every bit is meaningful.
There have been a few ways to solve the problem of sending lossless data across compression connections--the most popular of which is (drum roll) don't bother. At least that's what I most often see. But there are plenty of boxes out there that "listen for CNG tone" (fax machine's CalliNG tone used during the handshake prior to transmission) and, if detected, momentarily turns off compression for THAT call so that it can have the full and proper bandwidth to complete the call.
In my experience, CNG detection works pretty well. It's not flawless by any means, but it's gotten better over time. One thing that I have NOT seen is someone developing chipsets to detect modem calls. I suppose that's because fax machines still hold sway in most businesses today while modems largely do not.
But around the late 1990's, a bunch of talk about sending fax calls through the Internet began to pop up. The solution? Redesign the fax machine itself! We'll stick an Ethernet port on the back of it, change the standards in which it's data is sent, popularize it so that everybody makes and buys one and Voila! Problem solved.
A variant of that idea is to continue using standard old-fashioned fax machines, but have them make and receive calls through a FoIP gateway. These gateways basically have a split personality in that they speak the language of both PSTN (regular phone lines) as well as manage an IP uplink. It also does the job of converting the in/oubound transmission between the two interfaces.
Does that help? That and a $1.25 might get you some scalding hot coffee made from overcooked, burnt smelling coffee beans. But that's another topic....
Tim Alberstein