So a rough timeline:
Early on, Microsoft made .Net Framework.Net Framework as their development framework for Windows ecosystems. No support for unix at this time.
Years later they wanted in on the platform-agnostic action, and they made .Net Core.Net Core which tried to bridge this gap.
Not too many years ago they simplified the name, and released .NET.NET as a continuation of the platform-agnostic work.
This means that when you say .NET Core.NET Core, I must assume you're referring to the period in time before .NET.NET, which means you're several years behind the most modern developments in .NET and C#.