If someone uses a search engine (Google, Bing, Yahoo!, Duck Duck Go, etc.) to find content, they are using a search engine that gives results from across the indexed internet unless the visitor constricts their results.
If visitors to the York University webpages arrive via a search engine (eg. Google, Bing, or Yahoo!,) Google Analytics monitors their Keyword usage and reports it via the Keyword reports (Acquisition > Campaigns > Organic or Paid Keywords). The search engine is how they arrived at (were referred to) a specific York University webpage.
Google's Knowledge Graph
Depending on Keywords used, Google will display a Knowledge Graph along the right side of the results produced. It includes general information about a topic from a variety of sources. For example, check out the results for a search using the Keywords "York University".
If visitors are already on a York webpage and they use the search box that appears at the top of every page of the York website, they are using the York Search. It is powered by Google, but only consists of results within the yorku.ca domain. Google Analytics lists these results as 'Search Terms' and lists them in a separate section than the Keywords (Behavior > Site Search > Search Terms).