Long ago, but not so long ago ?, there is no difference between Data warehouse and Business Intelligence. During the inception of the Data warehouse, it is described as the capture, integration (ETL) and storage of data.
This data is not easily accessible by the non-tech savvy Business Analysts or the Data Analysts who want to do the analysis on their own without the help of IT to write the queries which were mostly static.
Software vendors noticed that there was a lack of good data access tools to query the data, and visualize it in a better way without any querying and easy to access GUI. So, the Business Intelligence tools were built and introduced.
So, if you had to make a one line distinction between the two, Data Warehouse describes the actual database and integration processes to populate it along with all the Data Quality rules, Business Validation Rules while BI describes the processes and tools to query, access, analyze and visualize the data.
To extend this for better understanding, Data warehouse deals with all aspects of managing the development, implementation and operation of a Data Warehouse or Data Mart including Metadata management, Data acquisition, Data cleansing, Data transformation, Storage management, Data distribution, Data archiving, Operational reporting, Analytical reporting, Security management, Backup/Recovery planning, etc.
Business intelligence, on the other hand, is a set of software tools that enable an organization to analyze measurable aspects of their business such as sales performance, profitability, operational efficiency, effectiveness of marketing campaigns, market penetration among certain customer groups, cost trends, anomalies and exceptions, etc. Typically, the term business intelligence is used to encompass OLAP, data visualization, data mining and query/reporting tools.
Some of the examples of the BI tools are Business Objects, Tableau, Cognos, QlikView etc.