ASP.NET is a framework developed by Microsoft to build dynamic web applications. There are two programming models to develop web applications using ASP.NET.
Both programming models use ASP.NET on the top of that.
ASP.NET is also a part of Microsoft's .NET Framework. We can write ASP.NET Applications code in any .NET Framework supported language i.e. C#, J#, F#, VB etc.
ASP.NET applications can only be hosted under IIS Server which is available on Window Operating Systems only.
Microsoft has now moved it's further development from this traditional .NET Framework (Windows only) to new .NET Core, which is Cross Platform (supporting Windows, MAC OS, and Linux) framework to develop software applications i.e. Desktop, Web, Console, Mobile Applications.