VBA stands for Visual Basic for Applications and so is the small "for applications" scripting brother of VB. VBA is indeed available in Excel, but also in the other office applications.
With VB, one can create a stand-alone windows application, which is not possible with VBA.
It is possible for developers however to "embed" VBA in their own applications, as a scripting language to automate those applications.
Edit: From the VBA FAQ:
Q. What is Visual Basic for Applications?
A. Microsoft Visual Basic for Applications (VBA) is an embeddable programming environment designed to enable developers to build custom solutions using the full power of Microsoft Visual Basic. Developers using applications that host VBA can automate and extend the application functionality, shortening the development cycle of custom business solutions.
Note that VB.NET is even another language, which only shares syntax with VB.