.NET Core vs .NET 5.0

What is the difference between a .NET Core 3.1 application and a .NET 5.0 application?
If we convert my .NET Core 3.1 application to .NET 5, will it still be a .NET Core application?
We are trying to understand if going from .NET Core 3.1 to .NET 5 is a Framework change or if it's just the new name for .NET Core and .NET Framework combined.
.NET 5 is the successor to .NET Core 3.1.

• Put the names aside for a minute. If you upgraded from .NET Core 3.1 to (a hypothetical) .NET Core 5.0, what would you expect to happen?

• .NET 5 is just .NET Core 5.0, but renamed to remove the "Core".

• Things that worked in .NET Core 3.1 should continue to work, unless there were intentional breakages between 3.1 and 5.0.

• .NET Framework 4.x is dead. It will continue to get security fixes, but the new line of focus is .NET Core 3.1 and the newly announced successor to .NET Core 3.1: .NET 5.0.

.NET 5 is not "core and framework together". There is no more Core. There is no more Framework. Install .NET 5 on your machine with Visual Studio and create a new project using a .NET 5 template and see which configuration mode is used. Read the many, many articles MS has published about .NET 5