This is a short explanation, searching on some of the terms will lead to further guidance.
The R stands for relational, this term was used by Edgar Codd when he first worked on the theory of data storage, he used the word
relations whereas nowadays they are normally called
tables.
Any data storage system is by definition a database, it could be a set of index cards, an address book or a set of files on a computer. The relational database has a number of tables representing entities and these are linked using primary and foreign keys, such as Customer table that has a CustomerId and an Order table that has the CustomerId as one of its columns, relating the order back to the relevant customer. Many electronic databases nowadays use different models, for instance an object database stores entire entities and often their children as single instances rather than shredded into different tables and columns, an XML database stores XML documents in their entirety.
Actually your question referred a DBMS/RDBMS, the MS part means management system so literally SQL Server and Oracle are systems that manage databases rather than the actual databases held in them. Nowadays the terms are often used interchangeably in the sense that people talk of a SQL Server database rather than a database managed by SQL Server.
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Joe (
Microsoft MVP - XML)
DBMS vs RDBMS
