"ASP.NET" is the name of Microsoft's .NET web platform. To answer your rhetorical question, ASP.NET MVC is an MVC framework for Microsoft's .NET web platform. "Microsoft MVC" would not be clearly constrained to web development.
What does that even mean? In this case, a bunch of libraries and a protocol for dispatching HTTP requests to .NET code.
If I use Mono's XSP server, and use it to host a ServiceStack backend, am I using "the ASP.NET platform"? It's 100% non-Microsoft open source. Am I using ASP.net when I host the same backend on IIS instead? Or when I host ASP.NET MVC (which is just a library) on Mono/XSP?
First 4 words of content at https://github.com/mono/xsp are "Mono's ASP.NET hosting server". So yeah, you're using ASP.NET. In the same way that working with Mono is using .NET.
Or maybe not. Perhaps someone means to specify that they're using Mono/XSP as opposed to one of Microsoft's implementations. But then it'll probably be obvious from the context.
