ASP.NET is Microsoft’s web development framework for building websites, APIs, and web applications. The modern version, ASP.NET Core, is open-source, cross-platform, and runs on Windows, Linux, and macOS.
ASP.NET Core 5 now has a single-aligned web stack for MVC and Web API. The image below shows no options to select Web API in the MVC project for ASP.NET Core 5, while ASP.NET MVC 5 gives the option to add Web API. Recommend reading through this if you want to learn about ASP.NET Core Web API .