Have you seen Twitter's "Sponsored Tweets", Facebook's "Sponsored Stories", Amazon's "Inspired by your browsing history". Ditching the word "advertising" is nothing new and we all use sites like these every day.
- "promotional material" = advertising material (that promotes a product)
- "discovery" = discovery through recommendations from the page owner
- hence, "promot-" + "discovery" communicates "advertising through recommendations"
However, "promoted" isn't quite the same thing as "promotional". What's actually happening is that promotional material is being presented as "recommendations from the page owner". The "discovery" itself isn't "promoted" (what does that even mean?). Most importantly, "promoted" doesn't contain the implication of advertising/sponsoring that "promotional" does.
It would have been more accurate to call this Sponsored Discovery or, to be even more real, Sponsored Recommendations. "Sponsored", however, is a bit of a dirty word too, and they probably made the call to euphemize around it, resulting in the confusing term Promoted Discovery.
"Inspired by your browsing history" are not ads. It is exactly what it says.
The Amazon example doesn't apply at all, as its internal linking to products. External advertising is clearly labeled as such on Amazon, too.
Disqus shows their advertising on a site of a different person. This changes a lot and makes this especially nasty.