Both are complete languages, capable of a variety of tasks. Visual Basic can be used to create web-based applications, and vbscript can be used to create client-side applications. Indeed, a number of famous and widespread worms were written in vbscript, taking advantage of Outlook and Outlook Express’s lax security when it came to vbscript programs.
Commonly, however, vbscript is used as part of the ASP infrastructure to generate web pages. vbscript is similar to php in a great many ways, none of which are complementary to either language.
Visual Basic is most commonly used for GUI programming for windows programs. It was remarkable originally due to the development kit that Microsoft sold, which made creating a GUI a simple drag and drop process. This was a subject of criticism by some, who worried about a drop in the quality of code that might result from such a lowered barrier to entry for new programmers.
Fortunately, ASP and Visual Basic are now obsolete, replaced by ASP.NET and Visual Basic.NET, both of which are considerably better designed than their predecessors.
Modern Visual Basic.NET is quite similar to Java, though many Java programmers are loathe to admit this.
Trivia: vbscript is one of the only languages besides javascript that can be used to do any client-side scripting in a web browser. Almost noone does this in practice because unlike javascript, which has a robust standard and many independent implementations, Internet Explorer is the only modern web browser to support it.