Well, think of them in the same way as different types of image. You have PNG, JPeg, GIF, SVG, EPS, and so on. Each format was created at a different time to fulfill different needs. Some are more complex, others are simpler.
MODs are the earliest (and simplest) common files you'll find. They're created using a bunch of different programs, including ProTracker and ModEdit. The term "Mod" also refers to any of the formats.
S3M is the ScreamTracker3 format. It's kinda like a super-enhanced MOD.
XM is the FastTracker II format. This was a revolutionary format when it came out, because it has some really neat features, like instruments (different samples for different notes automatically), envelopes (you can control exactly how the sound is going to change for every note without using effects), and much more besides. XMs are more similar to MODs than they are to S3Ms.
IT is the Impulse Tracker format. This is, in my opinion, the best of the old formats. It took many of the features from FastTracker and expanded on them; it boasts features such as New Note Actions (NNAs), filters, and a whole lot more besides. Note that there was (still is, I guess) a lot of controversy of which is better - XM or IT.
Now, if you're going to use Modplug Tracker (OpenMPT), you have to realise that
it's IT format is
completely different from Impulse Tracker's. OpenMPT has taken the IT format into the twenty-first century with plugins, automation, tunings, and a thousand more things besides.
Hope that clears things up a little. Remember that most modern trackers (like OpenMPT) can open most of the old formats, and play them back. OpenMPT can also convert between them (although moving up the chain [MOD->S3M->XM->IT] works a lot better than moving down the chain [IT->XM->S3M->MOD].)
