I find myself trying to explain this a lot, so I thought I’d put it “in writing” for future reference. This is not intended as a technically complete answer but a starting point to understanding what these terms refer to.
I usually start this by saying “Microsoft is bad at naming things”. The .NET Framework (.NET is a pretty bad name to begin with. Even DotNet would have been better. Who comes up with a name that begins with a period?) has been around since 2002. It evolved through many versions but around .NET 4.6 – Microsoft came up with a replacement framework that they decided to name “.NET Core”. It’s much easier to understand this with a visual, so take a look at this timeline in this Tweet – https://twitter.com/buhakmeh/status/1250127850457440256.
The .NET Framework versions are in green. Then came the .NET Core versions in purple. Understanding the version sequence is confusing. For instance, .NET Core 3.1 is newer than .NET Framework 4.8.
After .NET Core 3.1 – Microsoft decided to eliminate “Framework” and “CORE” and just call it .NET (starting with version 5). Since this timeline was produced, .NET 6 and .NET 7 have been released and .NET 8 is on the way. To be clear, .NET 5 and above are the later versions of .NET Core with the name changed. There won’t be any .NET Framework versions delivered after 4.8.
Short version:
.NET Framework is the older technology
.NET Core is the newer technology. Starting with version 5, they dropped the “Core” but you can think of .NET 5 as .NET Core 5, and .NET 6 as .NET Core 6, etc.