Well, the answer to that has changed over time as SAPs strategy has evolved. In the beginning, we had SAP BW. Shortly after that, SAP BW was bundled with other components, such as SAP Workplace (and later SAP Enterprise Portal) to form a licensed product that was named mySAP Business Intelligence (mySAP BI), to distinguish between the overall solution and the underlying SAP BW component.
With the development of the SAP NetWeaver, it was determined that the business intelligence component should become part of this platform. A decision was made to retain Business Intelligence as the name of the underlying component, because this name is more descriptive of the scope of the product, including as it does data warehouse management, extraction, transformation and loading capabilities, business modeling, business content, OLAP analysis, data mining, business insights via alerts and reporting features, and planning functions with the new BW-BPS.
Within SAP BI, SAP BW remains the core product, providing the ability to control, monitor, and maintain all processes connected with data staging and processing. However, this is a technical distinction that is expected to end with SAP BW 3.5, the business intelligence component of SAP NetWeaver 04. Future releases are planned to have only the Business Intelligence designation, such as SAP NetWeaver Business Intelligence 7.0, which is expected to be the name of the component in the next release.
What does this mean to you? You should start thinking of the product as SAP BI and try to use the term SAP BW only when you are referring to a specific release, such as SAP BW 3.1 Content or SAP BW 3.5. Its going to be a tough adjustment, but if you start now, it will be easier when the SAP BW term goes away completely!