On what basis do the results fall under the Popular Searches and Recent Searches?
The information for search queries is collected on the Magento side and can be found here: Magento Admin Panel → Marketing → SEO & Search → Search Terms.
If the query is new, a new entry will be added; after each use, the number of 'uses' is increased. All these queries can be found in the search_query table.
When it comes to Popular Searches, these are the most relevant queries sorted by popularity from the same search_query table: