Hi there MillieNeon!
Since I wrote the article that you are referring to, let me try to explain a bit further. Yours is an excellent question by the way. The answer though isn't so simple. I have to be careful not to confuse the issue further so I will be stepping lightly here as I should.
Not too many years ago, all the various "security" type applications would make claims of removing only certain types of security problems. Those specific programs would also (usually) be named in some way as to bring to mind what it is that it would do for you.
As an example, some years back there were fewer and simpler problems which would plague users on occasion. Most often the complaints were of "spyware" and "adware". "Virus" complaints were a completely separate issue. And...at that time, there were several vendors that would market their product and name it in some way so as to have the consumer understand what it does just from it's name.
Some of those products I'm referring to were named similar to these:
Adaware, Spyware Doctor, Trojan Hunter...and of course, antivirus products were named in a similar manner such as "Norton Antivirus" and "McAfee Antivirus" etc. so you can see how a consumer would be drawn to a product because of the way it was named.
Now...since the consumer's understanding is largely driven by the "vendors" description of their products over the years, many novice users would get themselves into trouble by installing too many of these. Thus, the reason I wrote that article.
Now, let's get to it...the difference between an "anti-spyware" application and an "anti-trojan" application should be spelled out by the vendor really. Spyware and trojans can actually be courting each other but to remove them requires different methods. Some spyware can be avoided by security settings in the browser and can be removed when you close it.
Trojans on the other hand, are responsible for downloading "stuff" without your knowledge. Spyware doesn't do that. Spyware can, in fact, be placed on the computer without your knowledge but doesn't download anything else as a part of it's intended action. Trojans do. I hope that clears it up for you.