Yes, you are right.

The old stuff, now no longer supported, is:

• .NET Framework up to and incl version 4.8
• Runtimes distributed as part of Windows
• Mono is a Linux Runtime used for compatibility

The new stuff:

• .NET Core, up to and incl 3, more recent versions are named .NET from version 5 onwards (to prevent mixing it up with the old Framework)
• Is completely cross-platform, natively
• I don’t know about desktop specific graphical stuff but that probably depends on the specific library