Thanks, all, for the kind words!
Nice question, not because it's really necessary to know the names, but for the explanation of where the names come from.
I think that knowing the terminology is already important in itself.
When you want to learn about performance optimization, you will read whitepapers and blogs, watch training videos or attend conferences. In all those situations, these terms will be used. So you will need to know what they mean. I have two more questions lined up on join operators, and I will use these terms in those questions.
Ed Wagner (11/20/2015)
An interesting question. I guess I don't see where any of it is in the execution plan itself.
Not directly, but there are indirect references to it. A Hash Match join operator will always have a "Hash Keys (Build)" and a "Hash Keys (Probe)" property, to describe which column or columns from each input is/are used to drive the hash-based matching algorithm. And a Nested Loops join operator can sometimes have an "Outer References" property that tells which data from the outer input is referenced by the inner input.