Databases typically aggregate collections of electronic journals, ebooks, and articles to which full-text is available. Examples of library databases are Discovery, Academic Search Complete, Business Source Complete, IEEE Explore, ACM Digital Library, etc. These databases bring together a collection of materials that are searchable via one interface with links to the full-text of articles or chapters.
An Index is a database of citations, often including information about articles such as abstracts. The Full-text may be available in another database or you may need to request the material though InterLibrary Loan. Most indexes will have a "Find It" button that allows you to link to other MSU resources and the online catalog. An example of an index is the rich bibliographic database Scopus.