RDBMS composed of several elements:
- Transaction manager -- manages transactions, as evident from it's name:)
- Physical storage manager -- manages how data stored in underlying file-system(s)
- Query parser/planner/executor -- this is 'user front-end' of database
Each of these elements is essential for any RDBMS and use different set of algorithms to make itself work.
If you interested in internals of RDBMS, get yourself this book: http://www.amazon.com/Database-Systems-Complete-Book-2nd/dp/0131873253/