You can access the data search from our search page, or from the search field in the upper right corner of every MusicBrainz page (which uses indexed, non-advanced search).
The indexed search is used by default. It uses the SOLR search engine, making it much more powerful than a direct database search, and, if the "advanced" option is chosen, allowing all kinds of specific queries via its advanced search syntax.
Popular results are preferred over exact matches. To search for exact match, please surround your search with double quotes, as in "Bach" for example.
Note: It can't find results that haven't been indexed yet, but indexation now run within seconds, see blog post.
The direct search searches the database directly: it can only carry out simple keyword searches with no boolean logic, but it is always up-to-date.
Note: It is just a fallback method, in case something goes wrong with the SOLR search server.