There are actually four types of databases for the search functionality in SharePoint 2013.
- Crawl Database
- Search Administration Database
- Link Database
- Analytics Reporting Database
Crawl Database - It stores all the crawl related information, such as the last crawl time and the last Crawl ID.
Search Administration Database - It contains the search configuration settings, such as the search topologies, mapping between the crawled items and the metadata properties.
Link Database - It stores information such as the search clicks along with storing information obtained from the Content Processing Components.
Analytics Reporting Database - For generating reports on the search related information and usage analysis, this database is used.