From what I can gather, the term "trolling" originated from the term "trawling", a form of fishing in where you drag a net behind a moving boat. So in other words, trolls work by deliberately antagonising people on forums, just to see who "bites" and gets dragged into a fight. Like Evil Sims who get "Fiendishly Delighted", a troll will take pleasure in just seeing how much grief he can cause and how many people he can offend. An inappropriate post can be similar, but usually results from someone getting too emotional and saying something rash. Rather than being offensive for the sake of it, the poster might be rigidly defending their political views, casually expressing prejudice, angrily criticising someone on the forum and so on. In short: Trolls are out specifically to stir up trouble, and inappropriate posters cause trouble by lack of civility. In shorter: what mtglady said.
In-game, I think 'Make Inappropriate Forum Post" and "Troll Forum" are the same thing, they've just been given different names to reflect the associated traits. Kind of like how "Have Evil Shower" is just a renamed version of "Have Shower", just because it seems more like something an Evil Sim would do. From what I've experienced they don't get different responses, although I could be wrong. Hope that's helpful.