Sadly, Visual Studio and VS Code are two completely different software's. Visual Studio is an IDE (Integrated Development Environment), this means it has more features than a normal text editor (for example VS Code or Atom). VS Code is a text editor, however you can install extensions to make it more into an IDE.
The best solution is to look at VS Codes market place and try and find an extension that will auto complete the HTML tags. I personally haven't found any extension for it.
Hope this helps, if you need any more advice or help DM me on discord CallumS005#9458 and I'll be happy to try and help.