This happens a lot and is part of a search engines consideration: What kind of industry / sector / line of business, or, as you name it, "category" can a site be correlated?
A strong signal for such an assignement are keywords, links, and more and more social mentions. Tools like from Sistrix compute this similar to give you a hint about your site (or your competitor's).
Example (btw, this is for stackexchange):
What is it good for? If your site is related to a specific industry, say "Sports" and gets lot of links from hairdresser or gardener sites (...) those can be easily devaluated. Links from "matching" sites will pass more link juice.
Every piece of (quality) content you create onsite will support your overall theme.
[Update / see comments] Sources:
SEOMoz - Best practices for SEO - external links / relevancy
Search Engine Watch / Relevancy
Identify quality domains / relevant contexts / link building
To answer the last of your questions: In theory it could be prioritized if your content or your site is already considered as an authority on that topic, or if the content outranks the other because it is considered as the unique, older or more trusted source. It the page that "mentions" the other is not that helpful as the other it might not be considered.
Even more: If the search term results in a SERP with universal search elements or local results (maps, videos, images, g+ / authors, product recommendations) it's less likely for your just-mentioning-page to get listed (this is not directly what you asked, just another aspect).