I installed .net core from this site. Playing with it led to a number of related package management questions:
dotnet restore
command proceeded t
I just found out that there's another location for NuGet packages used in .NET core projects. Its located at:
C:\Users\[User]\.nuget\packages
I think that this location contains regular .NET Framework packages.
Update: Thanks to brappleye3, here's a link to the documentation regarding dotnet restore.