.NET Core is not a rewrite in any way. It's the same runtime with the same GC and JIT, same language compilers and mostly the same standard library. It has just been stripped down by removing deprecated features (such as code sandboxing / partial trust) and made support non-Windows platforms.

You might have confused it with ASP.NET Core, the web development framework, which is a full rewrite.

If a developer confuses .NET Core and ASP.NET Core, is that a fault of the developer, or of Microsoft's nomenclature?

You are right, i was confusing asp.net core with .net core.

Hopefully these optimizations are for a particular version of .NET Standard and will see themselves in both .NET Framework and .NET Core.

Skimming, but it doesn't look like these optimizations are relevant to .NET standard (which is a formal specification of a set of APIs - not a particular implementation.)

Correct. Performance improvements are out of the scope of the standard. Much like how the HTML spec doesn't tell Google and Microsoft how fast their browsers need to work.