It uses Electron (the embedded Chrome wrapper) just like Atom does, but as far as I'm aware they dont share anything else that actually makes them an editor.
This is correct. VS Code is based off their Monaco Editor [0]
Actually, it's the other way around. From Monaco Editor's README [0]:
> The Monaco Editor is generated straight from VS Code's sources with some shims around services the code needs to make it run in a web browser outside of its home.
Monaco may now be built from VS Code source tree, but it is, IIRC, older than VS Code and was part of of Visual Studio Online (now Team Services) when it was released in 2013.
VS Code is the primary project now, but Monaco came first.[1]
Atom also added the Language Server Protocol (developed by VS Code) that provides a common API for implementing IDE features (completion, refactoring, etc).