Search engines describe their databases of web pages as 'Indexes'. Why? Search engines scour the internet for web sites and pages to present information to the searchers who use their search facility.
Most importantly, they want to present relevant results to the internet visitor who is on their site.
Just as importantly, web users these days are very impatient and they want answers quickly.
The 'index' helps the search engine to do this. After their software has visited sites - or crawled or spidered them - as it is now known, the search engine has to file the data in a way that it can be retrieved quickly.
So they code it and structure it in such a way that it can be retrieved and presented quickly in the search engine results pages - that's why it's an 'index' - not simply a database.