You're not alone; sometimes even the commentators, who have the same "over-the-shoulder" long-lens view that the folks at home do, will simply refer to a pitch as a "breaking ball" if it drops sharply or curves outside, even though a number of specific pitches can do that.
The fundamental theory of pitching is that the batter gains an advantage over the pitcher proportional to his ability to predict the pitcher's next move, and conversely, the pitcher gains an advantage over the batter inversely proportional to the batter's ability to predict the next pitch. Your better pitchers have a number of weapons to accomplish this, but key to all of them is control over three elements of the pitch; speed (and thus timing), vertical axis (drop), and horizontal axis (slide).
From the very good diagram Dor linked to, here's a basic breakdown of the most common RHP's pitches as seen by a RHB:
The variation of speed and breaking action produces a host of possibilities, which a good battery can use to keep the batter guessing. A pitcher can also aim pitches differently to make them look like other pitches; a pitcher can throw a fastball high and fool the batter into thinking it was going to be a sinker or splitter, or can throw a two-seam wide and the batter may think it's an errant four-seam until it breaks back over the plate.
Batters like a variety of different pitches; exactly what the batter likes should be known by the pitcher and/or catcher, and a combination of what the batter flat doesn't like, and pitches that look like what he does like but then change, are generally the order of the day. From time to time a pitcher may give a batter exactly what he wants, hopefully when he's least expecting it; this is often necessary to avoid showing the batter the same pitch too many times, and a missed opportunity can also put the batter "on the tilt", throwing off their concentration as they mentally kick themselves.