I have read about the difference between .NET Standard and .NET Core, but I really don\'t know what the difference is, or when to choose a .NET Standard library project and
.NET Standard is a specification of .NET APIs intended to be available on .NET implementations. This enables to define uniform set of BCL APIs for all .NET implementations.
.NET Core is one such implementation of .NET Standard. .NET Framework is another implementation of .NET Standard.
Image from .NET Blog
Federicos answer gives you a graphical overview of how each framework evolve with versions. Take a look at below diagram from Microsoft Docs.
Targeting .NET Standard increases your platform support whereas targeting a particular .NET platform such as .NET Core (or .NET Framework) will allow you to use all the platform features for that platform.