Well, you've got a little blurred general picture there, which is a lot more than what with the majority of population can brag. But if you want to focus it, here:
You are correct about the self-contained structure of module files. It has been prevalent through the second generation of PC trackers until recent years when so-called 3rd generation trackers (and some hacks) have allowed using external, even pro level, plug-ins as real-time synthesizers, advanced samplers, effects and what-can-you-think-of.
Karsten Obarski's Ultimate Soundtracker introduced the .MOD format and tons of hacked versions made it somewhat of a standard on the Amiga although there were playback and implementation differences. ProTracker (written and maintained by several different people throughout the years), especially the final revisions of versions 2 and 3 eventually became the most popular .MOD trackers on the Amiga. You might be spot on about .MED, somebody else needs to comment on that though. I don't really know since my path went from C64 to the PC.
Until ScreamTracker 3 by Future Crew, PC trackers were mostly imitating 4-channel Amiga trackers with the rare exception of offering more channels a.k.a. polyphony. (Not that the processors could have handled mixing that much more nor that the consumer level soundcards, DIY DACs or the system speaker could have made it all sound any good. ;) ST3 and its module format .S3M grew immensely popular only to be matched later by Fasttracker II (by Triton) with its .XM and Impulse Tracker (by Jeffrey Lim) with .IT.
The early versions of IT were just an improved ST3, and for a very long time XM was still the format with more features. As time went by IT took over the features from FT2 and introduced new features as well. I guess Triton was just too busy programming games at that time ;)
FT2 was the first tracker to really leap ahead from the old regular module formats which only offered samples without any fancy instrument attributes like envelopes, auto-vibrato etc.
