The .NET MVC thing is off.

ASP.NET MVC is a web framework that implements the MVC pattern, as opposed to ASP.NET Web Forms, which was control based. ASP.NET MVC versions 1-5 run on the full .NET framework.

ASP.NET Core includes MVC, and the API has stayed as close asp possible to previous versions of ASP.NET MVC. The lower level bootstrapping / hosting / middleware / config stuff is pretty different (much improved, IMO), but your application code (models, views, controllers, services, etc.) should move from ASP.NET MVC to ASP.NET Core pretty smoothly.