The reason that .NET Standard exists is for portability; it defines a set of APIs that .NET platforms agree to implement. Any platform that implements a .NET Standard is compatible with libraries that target that .NET Standard. One of those compatible platforms is .NET Core.
The .NET Standard library templates exist to run on multiple runtimes (at the expense of API surface area). Obversely, the .NET Core library templates exist to access more API surface area (at the expense of compatibility) and to specify a platform against which to build an executable.