There are three differences:
A difference: the meaning is not the same.
Visual Studio (abbreviated VS) is Microsoft's US development kit series, is a basic complete set of development tools, which includes most of the entire software life cycle tools needed, such as UML tools, code control tool that integrates development environment (IDE) and so on. Popular speaking, is a compiler.
visual studio code is a project of Microsoft Corporation in the United States: runs on Mac OS X, Windows and on Linux, to write for cross-platform source code editor modern Web and cloud applications. More simply, it is an editor.
Difference between the two: cross-platform capability is not the same.
Visual Studio various functions will only run on Windows and macOS (Mac OS X), jump across platforms can not be edited.
visual studio code is a true cross-platform editor, can be used on user habits platform, and not have to migrate to Windows.
Three differences: function is not the same.
Visual Studio is the most popular Windows application platform integrated development environment. It provides advanced development tools, debugging features, database functionality, and innovative features that help to quickly create the most advanced applications, the development of new programs on a variety of platforms.
visual studio code integrates all the features of a modern editor should have, including syntax highlighting, customizable hot key bindings, bracket matching, and code snippets collection, this editor also has a ready to use out of the box to Git support.