Medicines almost always have two names: the brand name, and the generic name. Tylenol is the brand name for a medicine containing acetaminophen, and Motrin is a brand name for a medicine containing ibuprofen. I always try to learn the generic name, because the same active ingredient can often be found in different brands, and I like to know what exactly I'm getting. I started learning generic names so I could identify whether store brands contain the same medicine as the more expensive brands, but I have found it useful in other cases as well. For example, there are various kinds of pain medications, most of which contain some combination of acetaminophen, ibuprofen, and aspirin; by looking at the exact contents, I can tell what I am actually getting.
Another type of medication with a confusing variety of choices are antihistamines and decongestants (which are often combined in the same pill). The only one that ever seemed to work for me was Actifed, but one of its active ingredients, pseudophedrine, was placed under restriction a few years ago because people were converting it into methamphetamine. Actifed was unavailable for a while, and then, when it came back, it didn't have the same effect on me. I discovered that, contrary to what one would expect, they had done away not only with the pseudophedrine (the decongestant), but also with the triprolidine (the antihistamine), and were marketing a completely different medicine under the same name. It didn't take long to figure out that pseudophedrine was not the drug that was helping me, but I couldn't find triprolidine anywhere until a kind pharmacist special ordered some. It's marketed under a couple of different names, and it's actually very cheap, but you won't find it in any store that I've seen.
As a side note, I would like to say that this is a perfect example of unwanted government interference. I am ambivalent about the war on drugs, but I am clear on one thing: I don't want my right to an effective medicine to be curtailed because some people are turning a beneficial chemical into something that they can get high on.
“Anybody gone into Whole Foods lately and see what they charge for arugula?” --Barack Obama (link)