Yes, FMX is also called 'cast iron cruise-o-matic' The only thing is that they changed the positioning of the shift pattern to the more common or standardized 'P-R-N-D-2-L' instead of the earlier 'P-R-N-2-D-L' or whatever. My 1966 Comet (also a Mercury) has the earlier shift pattern on its cast iron cruise-o-matic. I have to read the manual every time I try to drive the thing to make sure I'm putting the gear selector in the right position for 'Normal' Drive! (I really haven't driven it all that much since we got it back in 1988. We've probably put less than 500 miles on it since then!)
Internally, the FMX also does not have a conventional neat and tidy valve body inside the trans like a C-4 or C-6. It has a bunch of metal tubes running all over the place that makes the inside (pan view) look like brains or some 1950s demented sci-fi creation.
I'm surprised that you know about C-3s. Here in the States they were mainly used on the smaller 4-cylinder economy cars like Pinto, Mustang II or other such. Even the 2.8 litre V-6 Pintos got C-4s.
Then there is the C-5, which I'm told is basically a C-4 with a provision for a lock-up converter.
When we get to the AOD, AOD-E, E4OD, A4LD and all of the front-wheel drive transmissions I tend to get lost. The AOD is the 'normal' overdrive automatic trans used from 1981-1991. The AOD-E is electronically controlled, but basically an AOD, used from 1992 to the present. The E4OD is the heavy-duty piece, really an overdrive C-6, and many of the C-6 internals were carried over.
There are a few transmission specialists here on MercuryCougar.net that can answer your transmission questions better than I.