.Net Framework (older) and .Net Core (current) are the two different implementations of .Net from Microsoft.

.Net Framework is for developing Windows and Web application for the Windows platform.

.Net Core (now .NET) is a cross-platform and open source framework for building applications which can run on Mac, Linux or Windows. It is not an extension of the older .Net framework, but is completely rewritten.

The below release versions table may help to understand the version nos. used for the two frameworks.

.Net Standard is a set of .NET APIs that are available on multiple .NET implementations. You use .Net Standard only when you have to share code between older .Net frameworks and the newer .Net versions. For more info refer: https://learn.microsoft.com/en-us/dotnet/standard/net-standard?tabs=net-standard-1-0