A BI Platform/Suite will be more of a full-stack solution that will usually include the following:
- ETL Tools
- Data store / database
- Multi-dimensional database / cubes
- Tools to author the MDDB as Dims/Attributes/Facts/Measures etc
- Reporting tools / platform
- Analytics tools / platform
- Dashboard tools / platform
So it's basically an End To End BI solution where all the pieces are built to fit together very well. Examples of this are the MS BI Suite (with MSSQL Server, SSIS, SSAS, SSRS, BIDS, PerformancePoint, Excel etc...) or the Pentaho BI Suite if you like your open source. Other big players in this realm are SAP, Oracle and IBM.
A Dashboard Tool is just one of those components. It doesn't do any massive calculation or ETL function, it's basically a presentation tool. It takes data, and turns it into pretty information.
Some examples are PerformancePoint, MicroStrategy.
tldr: BI Platform is for full stack, E2E BI development, Dashboard Tools are just for presenting data and making pretty dashboards.