The radio does not need to be Mustang specific. It just needs to be the premium style with line-outs and not the older non-premium style radio.
Below is the premium style connections. Power connections to the left. Top plug on the right is the slave/CD changer connection. If not in use you need that jumper on top of the case in place (except 1993 mustang). Middle are the 4-channel low-level line outs to the amplifier. Bottom is 2-pin steering wheel audio controls.
By comparision, here is a non-premium radio. right plug are the speaker outputs. These radios have internal amplifiers. This type will not work.
There are other makes and models that come with premium style radios that will work fine. Most of the compatible ones are from around '92-'99 time period. Ford phased out of that radio style around '00 (give or take a year or so). There are some limitations however like the windstar radio, but at this time that's the only one i'm aware of that will not work on the Mustang. The differences in part numbers reflect mostly cosmetic differences such as faceplate style (rounded or square corners), display color (blue or green) and if the radio gets a 6th preset or clock button. There were also some internal upgrades to the tape deck mechanism. The radios themselves are backwards compatible even if not physically able to swap parts. I'm simplifying a lot here, but i've pulled apart dozens of these radios over the years to rebuild/repair them.
Photo in post #5 is a '99 Contour CD player running the original Mustang slave CD player. It works perfectly. Slave cd player functions as you would expect. I ran that for a few weeks until i had a chance to rebuild my failed original head unit. I've recently swapped the tape player back in (to run a bluetooth cassette), but it's actually a 1993 Lincoln Mark 8 unit, with the tape player from a 1994 town car. Works beautifully.
You can even run the '91-97 Ford/Lincoln 10-disk CD changer off the original head unit. (if you can find one). I've done it. I currently have the CD changer installed in my Fox Mustang, but have been debating moving it over to my Sn95 where it would get a lot more use.