What is .NET Core?

It is a cross-platform implementation for running websites, services, and console apps on Windows, Linux, and macOS

Does .NET core open source?

Yes, it is an open source and its available in git hub https://dotnet.microsoft.com/platform/open-source

What is Xamarin/Mono?

It is a .NET implementation to run on all major mobile application platform (Android, iOS)

What is .NET standard?

It is a formal specification of .NET APIs that are available on multiple .NET implementations. i.e., it logically groups the different .NET API implementation (.NET standard, Core, Mono, Xamarine) for ease reference 

For latest update refer official Microsoft site https://dotnet.microsoft.com/platform/dotnet-standard

What is the difference between .NET framework VS .NET Core?

1) .NET framework runs only on Windows platform whereas .NET Core run across all platforms (Linux, Mac, Windows)

2) .NET framework installed per computer with all Base Class Libraries (BCL) whereas .NET Core run per application and required  libraries can be installed using Nuget package manger thus .NET core application is lightweight than .NET framework application

3) .NET framework application uses GAC assembly whereas .NET Core uses Nuget package (more technical of above point 2)

List few important .NET Core CLI commands to create, build and run an .NET core application ?

1)To create a new application

dotnet new <<applicationtype>>

dotnet new console  (to create a console application)

dotnet new mvc       (to create a mvc application)

2) To build an application

dotnet build (make sure to be inside the dotnet core application folder)

3) To run an application

dotnet run (make sure to be inside the dotnet core application folder)

How to create a .NET core application using Visual Studio IDE?

1) Download Visual Studio Express edition (2017 and above) https://visualstudio.microsoft.com/downloads/

2) File => New => Project => Visual C# => .Net Core => Console (or) ASP.NET Core Web Application

What are all the different families of .NET framework libraries available?

1) .NET framework  

2) Mono (Xamarine)

3) Silver Light

4) .NET Core

5) .NET Compact

Do we have a .NET framework library which should be compatible for all families of .NET framework?

Yes, Microsoft provides a library called "Portable Class Library" (PCL).  You can create a new project by choosing "PCL" 

i.e., Visual Studio => New => Class Library (Portable)

Note: PCL libraries no longer possible to create a PCL library with Visual Studio 2017 as they've been replaced by .NET Standard libraries Refer PCL profile with .NET standard library mapping at https://github.com/dotnet/standard/blob/master/docs/versions.md

What was the challenge when using PCL?

Every time any framework level changes or new framework introduced needs recompile of entire project by scoping those changes

Can you provide a concise overview of the different families of the .NET framework and their usage perspectives, considering the continuous evolution of the framework?

Agree, and let me try to summarize it for ease understanding

.NET Framework => Its the original one which works only on Windows platform (Windows & Windows Server).  Still few applications are continue to run in .NET framework with out upgrade to latest (will explain what is latest below)

Mono => Its a cross-platform implementation of .NET Framework which is open source.  It currently supports Android, iOS & Web Assembly development

.NET (Core) => It refers to modern .NET which is open source and cross-platform.  It mainly focused for cloud age applications but major part of the libraries compatible with .NET Framework

So when you develop or talk new application then simply go for .NET 8.0