Would a simple way to remember the difference be that perspective lines exist in 2D drawings and images, while parallel lines exist also in reality?
Also to point out: rarely do people genuinely "appeal to Wikipedia". Rather, Wikipedia is a starting point. It has references to more in depth studies. The information in there has been peer reviewed and verified.
It's a big difference to "appealing to Sam" - he's just one man, with some far out, unverified ideas, and very often shown to be wrong.
Likewise, no one's really "appealing to the ancient Greeks", but rather referencing them as the discoverers/inventors of something we have tested over and over again, and can test again today, if we like.
Does that make sense?