WolframAlpha is different to the examples of databases listed because it is an answer-engine. It is different to search engines like Google because it provides one answer to the question/search, as opposed to search engines which provide you with a broader range of results. The difference with the rest of the examples is that it can only be accessed online.
A database is a collection of related data, organised for convenient access. It is organised in a way that it is easier to find and select a desired piece of data. It is somewhat of an electronic filing system. In order to access a database, a Database Management System (DBMS) is required. This enables you to select, organise and edit/enter data in the database.