I'm a little confused on the structure of the .NET framework. Each website I've visited (and book I've read) has a different take on this. Not only that, but there are dozens of elements that start with the name "Common".
Let's see if I have this straight. The CLR and CLI are completely different entities. CLI is a set of standards (and submitted to the ECMA for standardization), and the CLR is a platform in which CLI compliant code can be managed and run.
If this is correct, where does the Base Class Library fit in? It is it's own separate entity, or a part of the CLR or CLI?