What is Difference Between .Core CLR VS Mono CLR? Then why Microsoft maintain different run time environments ?
Both are implementations of the .NET Standard but they have different implementation details. Mono is historically grown by the need of a cross-platform .NET implementation that runs everywhere. Later Mono became the foundation for Xamarin.
.NET Core is designed for performance, cross-platform, scalable cloud scenarios and the main workload is ASP.NET Core that runs on it. It's true that both are similar in the API surface and cross-platform capabilities, but they were created with other requirements in mind.
Both framework implementations are well supported. Depending on what you need to do, you pick one of them:
.NET Core
Mono