I was wondering what the difference is between installing Visual Basic and Visual Studio?
Visual Studio is the integrated development environment (IDE) used to create programs in Visual Basic or the other 'Visual' named languages. So in that sense, it doesn't quite make sense to compare the IDE to the programming language: Visual Studio is like the text editor, Visual Basic is like the language you are writing in.
However, when you download Visual Basic Express, you are really downloading Visual Studio Express with appropriate components to make Visual Basic programs. It's called Visual Basic Express in the Start menu and the title bar, even though it's really Visual Studio Express underneath. So in that sense, your question may really be "What's the difference between Visual Basic Express (Visual Studio Express) and Visual Studio?"
There are several different editions of Visual Studio, starting with the free Express editions and then continuing with the Professional, Premium, and Ultimate editions that cost money and have additional features. You can look at the Wikipedia article Microsoft Visual Studio for a description of the different editions and a comparison chart. Or you can look at Microsoft's Visual Studio Products page for a comparison chart of the commercial versions. (Express isn't shown in this comparison.)
Visual Basic is a event driven programming language, it is just like basic(coding) the difference is that it has buttons, textboxes, etc basically graphics that are programed to conduct an action.
Visual Studio Is a software development environment (also know as an Integrated Development Environment or IDE), It's used primarily by Software Developers to build Software products, websites and Utilities. Visual Studio was introduced by Microsoft in 1998.