Tetracycline is an antibiotic, so it kills stuff in your gut. Not all of it, but it is best to take probiotics if you're taking any kind of antibiotic just to keep your gut flora a little happier. It also kills the bugs that tend to be the reason there's pus in acne, which are what cause acne to be red and bumpy

Accutane is like a roided-out version of vitamin A and works like vitamin A in your skin, just even more vita-tastically, or whatever scientific term is appropriate. This means that it clears up some of the causes of acne (makes your skin produce less oil, shrinks pores so they can't clog as easily, etc.), but it's so freakin' vitastic that it goes too far. All my friends on Accutane in high school needed lip balm 24/7 and a few of them had frequent nosebleeds, especially while playing sports. One of them had to go off it very soon after he started because it made his acne much worse and he ended up with a pustule 2.5 inches across on his back that needed to be drained and packed.

Inflammatory bowel disease is another thing that seems to pop up down the line for some accutane users, but AFAIK no formal causal link had been established, or perhaps heads are just in the sand. For what it's worth, one of the folks I know from high school that took accutane has been dealing with inflammatory bowel problems since shortly after she took it, which was around 20 years ago.

Very different drugs that work on acne from entirely different angles. Tetracycline won't cause long term gut health problems all on its own unless you take it for far too long, or at unsafe dosages.