All data warehouses are databases, not all databases are data warehouses.
Basically a database is any system which keeps data in a table format.
Here’s the definition:
“A computer database is a structured collection of records or data that is stored in a computer system so that a computer program or person using a query language can consult it to answer queries. The records retrieved in answer to queries are information that can be used to make decisions.”
A data warehouse is a specially setup database designed to hold large amounts of data for reporting purposes. While a normal database is optimized for transactional activity (while keeping a small amount of history) a data warehouse will be optimized for large scale reporting.
Within a data warehouse data from several systems will typically be merged together to present a global enterprise view. Data warehouses will also typically keep a very long history from several years to the entire life of the company so that very long term trends can be viewed.
Data warehouse identifies a number of characteristics that differentiate warehouses and marts from conventional operational databases. Virtually all of these have some impact on data modeling.
Database is an integrated collection of logically related records or files consolidated into a common pool that provides data for one or more multiple uses.