I know little of dotnet beyond trying various semirandom things to make some .net apps work on linux. With that out of the way, my understanding is that
- Originally there was .Net Framework, by microsoft, for windows only. Versions 1.0 -> 4.8 were released.
- Then mono came along as a somewhat clean-room reimplementation of .Net framework, focusing on making it run on Linux. Though mono does not implement windows gui widgets, so for that there's stuff like Gtk#. And you cannot run windows GUI applications on mono for this reason, even though the core parts might be portable. Eventually Microsoft acquihired the Mono team.
- Later on Microsoft made the core of .net open source and portable, creating .Net Core. Or .Net Runtime, linked above, which is apparently the same thing (not sure when they dropped the "Core" part of the name). Applications written for .Net Framework can't just be recompiled for .Net Core/Runtime, there is porting work that needs to be done. And similarly as for .Net framework, even though the core is portable and open source, the windows gui libraries are not. So again windows GUI applications written using .Net Runtime cannot run on Linux. Not sure if there exists anything like Gtk# for .Net Runtime, allowing creating native Linux GUI applications with .Net Runtime?
- Finally, we have wine which is an implementation of the Windows API on Linux. And in a wine environment you can install e.g. .Net Framework including GUI libraries, so you can run .Net GUI applications that way.
They dropped the "Core" suffix with v5 in 2020, since at that point there was no longer naming confusion.
While Microsoft doesn't have their own framework supporting Linux GUI apps on the modern .NET runtime (MAUI does Mac/iOS/Android but not Linux), there are third-party ones like Avalonia.
Dropping the "Core" suffix introduced more naming confusion. Before that, ".NET" was often used as a shorthand for the (now legacy) .NET Framework. Which makes googling for Core-specific things much harder than it needs to be.
It is harmful to write new code that targets .NET Framework and existing actively maintained applications all have migrated to .NET. The ones that did not either have poor maintenance or authors that lack time as they don't owe extra effort unless they want to do that (or sometimes it is a skill issue, unfortunately).
- Originally there was .Net Framework, by microsoft, for windows only. Versions 1.0 -> 4.8 were released.
- Then mono came along as a somewhat clean-room reimplementation of .Net framework, focusing on making it run on Linux. Though mono does not implement windows gui widgets, so for that there's stuff like Gtk#. And you cannot run windows GUI applications on mono for this reason, even though the core parts might be portable. Eventually Microsoft acquihired the Mono team.
- Later on Microsoft made the core of .net open source and portable, creating .Net Core. Or .Net Runtime, linked above, which is apparently the same thing (not sure when they dropped the "Core" part of the name). Applications written for .Net Framework can't just be recompiled for .Net Core/Runtime, there is porting work that needs to be done. And similarly as for .Net framework, even though the core is portable and open source, the windows gui libraries are not. So again windows GUI applications written using .Net Runtime cannot run on Linux. Not sure if there exists anything like Gtk# for .Net Runtime, allowing creating native Linux GUI applications with .Net Runtime?
- Finally, we have wine which is an implementation of the Windows API on Linux. And in a wine environment you can install e.g. .Net Framework including GUI libraries, so you can run .Net GUI applications that way.