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 Core is an implementation of .NET Standard. It's available on multiple operating systems, but that's not the same thing - there are other implementations of .NET Standard as well.
So if you create a .NET Core library, it will have access to things that are implemented in .NET Core, but aren't part of .NET Standard, and your library won't be compatible with other implementations of .NET Standard, such as Xamarin, Tizen, full .NET desktop framework etc.
In short: to achieve maximum portability, make your library target .NET Standard.
.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.
.NET Standard is a specification of APIs that all .NET implementations must provide. It brings consistency to the .NET family and enables you to build libraries you can use from any .NET implementation. It replaces PCLs for building shared components.
.NET Core is an implementation of the .NET Standard that’s optimized for building console applications, Web apps and cloud services using ASP.NET Core. Its SDK comes with a powerful tooling that in addition to Visual Studio development supports a full command line-based development workflow. You can learn more about them at aka.ms/netstandardfaq and aka.ms/netcore.
The above, together with a very clear explanation of most of the stuff discussed in this question can be found in the following extremely helpful article by Microsoft (MSDN - September 2017): .NET Standard - Demystifying .NET Core and .NET Standard
.NET Core Class library is basically a subset of .NET Framework library, which just contains fewer APIs. Sticking to .NET Core Class library makes it difficult to share code between runtimes. This code might not work for a different runtime (Mono for Xamarin), because it doesn't have the API that you need. To solve this there is .NET Standard, which is just set of specification that tells you which APIs you can use. The main purpose of .NET Standard is to share code between runtimes. And it's important that this specification is implemented by all runtimes. (.NET Framework, .NET Core and Mono for Xamarin).
So if you are sure that you will use your library only for .NET Core projects, you can ignore .NET Standard, but if there is even a tiny chance that your code will be used by .NET Framework or Mono for Xamarin then it's better to stick to .NET Standard
Also note that higher versions of .NET Standard contain more APIs, but lower versions are supported by more platforms. Therefore if you create a .NET Standard library that you want to share between runtimes then target the lowest version you can, which helps you reach the most platforms. For example, if you want to run on .NET Framework 4.5 and .NET Core 1.0, the highest .NET Standard version you can use is .NET Standard 1.1. Refer to this great table from the documentation for more info about it.
PS: Also if you want to convert your library to .NET Standard, the .NET Portability Analyzer could help you with that.
Did you mean .NET Framework? Because .NET standard is an implementations, such as .NET Framework, .NET Core and Xamarin.
I love .NET Core because we can host it on Linux (use nginx in my experience). It's different than .NET framework which is you can only host on IIS. You can consider about hosting budget in this case (Because windows server is expensive for me).
In the development environment perspective, .Net core is lightweight. So, you can use VSCode, Sublime, for IDE (not only visual studio).
In simple terms, .NET standard is used for writing class library projects which compiles to dll. .NET Core can be used for developing actual web applications which can run on all operating systems (Windows, Linux, MacOS). (In .NET Core 3 Microsoft has provide the functionality to develop desktop apps using WPF, but uptil now these apps will not be cross platform and will only run on windows system. In future Microsoft might make them cross-platform too) .NET standard libraries/dlls can be used in any application which uses .NET (.NET framework, .NET Core) which means that you can use .NET standard with both .NET framework and .NET core.