.NET Core was the name for the cross-platform version, but that's the default now and will be the future. No need to differentiate from the older Full Framework anymore.
Microsoft naming strikes again. I suspect they're only dropping the "core" now because they can - below 4 there's a need to disambiguate versus .net Framework versions.
Not to mention there is no upgrade path from .Net Framework to Core. Major missing features like WCF are still an issue in .Net 6.
Migrating is a long and slow processes. Luckily we can use .Net Standard 2.0 as a bridge for libraries.