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It's been covered by others here already, but my understanding, as an outsider reading all this, is that .Net Standard is like C99 or C++14, a standard or specification that defined how the language is to function, and then .Net Core is implementation, like GCC or Clang are compilers that implement the C/C++ standards. In the prior example given, Java has a standard for each version that defined how the language functions, and then there are virtual machines that implement that standard, such as Oracle's (originally Sun's) JVM implementation, OpenJDK, or in the distant past, the Blackdown Java port[1].

Contrast to languages where there isn't a spec, or the spec is the interpreter, such as Perl 5 (Perl 6 actually has a specification and multiple implementations or various levels of conformance), or things in between, such as Python with the Python Language Reference. There are benefits and drawbacks to a standard/specification. One benefit is that it's easy for someone to start their own implementation and test for conformance and have a high degree of surety whether it will work with existing programs. One downside is that when there's a problem found in the spec, it often requires more work to fix, as the changes need to propagate out to the implementations, which will have their own timelines as to when they can implement it.

1: https://en.wikipedia.org/wiki/Blackdown_Java