.NET Core is what it takes to do the runtime. However Visual Studio has designers, editors, debugging that is not part of the .NET Core runtime. So you would want to install .NET core support as a Visual studio component. As a bonus, when you update your Visual Studio, you will also get new versions of .NET Core as well. This is the same with Visual Studio Code. It's just that any extra features are part of the Extensions, so it is a bit easier to just pull what you need.
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