The intentions behind this series are to answer with a little bit of context or examples some of most commons C# interview questions.
Both are implementations of .NET runtime, the framework is the older one and core is the new cross-platform one, both share many components but not all.
This is a quick drop so I'll try to write about one or two more questions
This is the older implementation that is supported only on Windows machines, you should use it on apps that already use .NET Framework, some .NET technologies that aren't available in .NET Core like Reporting services or platforms that currently aren't supporting .NET Core like some parts of Azure (This is a transitional situation).
Currently .NET Framework is at the version 4.8.
The core is the new implementation of the runtime, cross-platform(And in 2020 you'll mainly use this).
The choice of the core can focus when your app needs to be cross-platform, you target microservices, using Docker, needs high-performance and scalable systems and you need side-by-side .NET versions per application.
Currently .NET Core is at the version 3.1.
Currently, in this transitional situation, there's no way of using a shared code library written in .NET Framework on a .NET Core application. To resolve issues like this .NET Standard arrived, which is a specification of set APIs compatible with both .NET runtimes.
Currently .NET Standard is at the version 2.1.
You can go deeper on the subject @: