One point I didn't make as strongly in my last article is that even though a fighter on top will often attempt to move to half guard, half guard is still a relatively advantageous position for the fighter on the bottom. It used to be considered a very weak position, but as MMA has evolved and fighters have gotten better at BJJ, more and more are taking advantage of the aggressive possibilities that can be used from half guard.
Mount: From a distance, mount looks like guard, but the fighter on top is truly on top, with their legs over the opponent's torse instead of trapped within their legs. With a mount, you've taken away the defense of a fighter's legs and put them squarely into desperation defense. This article's photo gives you an idea of why you don't want to find yourself on the wrong end of a mount.
If you put the ground positions along a spectrum, guard is on one end and mount (or back control) is on the other. Guard is the position most favoring the fighter on bottom, and mount is the best position for a fighter on top.
The fighter in mount usually will exploit their advantage with ground and pound, slamming shots into the opponent and forcing them to guess if they'll be going high or low without fear of getting hit themselves. Submissions are also easy from mount. Here's a great video from EliteCageFighting.com showing one of the more basic ones, an armbar from full mount.
Meanwhile, if you're on bottom, options one, two, and three are get out of there. You can't effectively strike under a mount and submissions, aside from the occasional fortunate armbar or kimura, are rare. Out of desperation, mounted fighters will sometimes attempt to roll out, giving up the back and leaving themselves in a different but equally rough position (although enabling them to turtle.)
Side Control: For the dominant fighter, side control is much better than being in guard, although not quite as powerful a position as the mount. It is, however, somewhat easier to get to from guard than a mount is since you're attacking one side of a fighter's body instead of taking them head-on. Here's an illustrative picture of side control; you can see that it's pretty much as it sounds.
Side control is a powerful offensive ground position for a muay thai fighter because the opponent's side is wide open to slam in big knees and elbows and weaken their base. It also exposes the arms of the fighter on bottom, leaving submissions open, and can be used for leglocks as well (although not nearly as much as say, an open guard). A fighter in side control will sometimes also look to get their legs directly over the torso, transitioning directly to mount.