A DBMS is a set of software programs that controls the organization, storage, management, and retrieval of data.
A database is a collection of permanently stored data used by an application or enterprise. A database contains logically related data, which means that the database was created to represent the real-world.
All databases are not built on the relational model, see Database - Model
When people use the word database, fundamentally what they are saying is that the data should be self-describing and it should have a schema. That's really all the word database means.
Why would I want a database? What problem do they solve?
- Sharing. Support concurrent access by multiple readers and writers
- Data Model Enforcement. Make sure all applications see clean, organized data
- Scale. Some work with datasets too large to fit in memory
- Flexibility. Use the data in new, unanticipated ways. Abstraction … Layer between physical and logical.
Documentation / Reference
- Bill Howe, PhD (Director of Research, Scalable Data Analytics) University of Washington - eScience Institute