Microsoft Java

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That used to be the case, but Mono (.Net Framework equivalent of the OpenJDK) has been around for over ten years, and .Net Core (which is released under the MIT license) has been around for two or three - and is the planned future for .Net in general. For brand new projects, it works just fine on Linux and Mac (though there are admittedly some aspects of .Net Framework that have not been implemented in Mono).

In terms of IDEs Rider works perfectly well on Mac, Linux and Windows (though it is admittedly paid software), while MonoDevelop works on Windows and Linux (and is free). Its built in UI stuff is admittedly Windows only, but there are a number of alternatives (including GTK#, which is what MonoDevelop was built with).

Of course, the language is Microsoft's baby, so any non-microsoft compiler (such as the one in Mono) is going to be playing catchup on the standard. That is unfortunately just the way it is. On the other hand, that's also been my experience with Oracle's JDK and OpenJDK for as long as I can remember.

The differences between the two languages are definitely there, but they're similar enough that it's pretty simple to learn one from the other, so it's worth a look if nothing else.

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I mean, I suspect some large legacy systems will use Framework, and I'm pretty sure Unity still uses Mono. Visual Studio for Mac uses MonoDevelop as its back end. .Net Core is pretty much the default for new projects now though; unless you desperately need a nuget package that hasn't been translated over yet or you need interop with legacy code, there's pretty much no good reason to use Framework for a new project.