A database is a searchable collection of records pointing to published information. Databases can store, index and retrieve information. For the purposes of your assignments, your tutors use the term databases to refer to database products from external suppliers. One example would be CINAHL. Some databases are free but the library subscribes to many others.  

Some other information providers can be on the dividing line between a database or a host service. A host service makes available many individual databases under one search system. If you refer to one of these when writing up your search strategy, you should name the individual database you have used, or name the subject search, an example of this would be the ProQuest Central service which covers individual databases such as PsycINFO, but if you did a more general search, you could refer to the ProQuest Social Science Search. If in doubt, check with your lecturer or Academic Development Tutor.
Some services are hosts, so don't refer to them as databases when writing up - an example would be EBSCO. 
Discover is best described in exactly these words. 
Internet search engines (like Google Scholar) also can be used to find useful information, but in academia they are known as search engines.

What information do they contain?

Some databases are general and cover all subject areas (like the Discover search on the main library web page), while others focus on a particular discipline. Some contain specialist subject information such as market research reports or industry standards. The key function of most of them is to act as an index to journal articles (or maybe individual chapters within a particular book). However, some may also find books and reports.

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SMILE by Imperial College, Loughborough University and the University of Worcester, modified by Marion Kelt Glasgow Caledonian University is licensed under a Creative Commons Attribution 4.0 International License.