I reread your original question in this thread more than once. I finally realized what you asked. So I went into my database to find the person who is a '1/2' relative of mine. 'Twasn't the man I thought it was. The 1/2 relative is in there somewhere but so far I haven't re-identified him. Sorry. At this time I can't run a test for you.
But - - The Kinship routine is only dealing with two people and to a lesser degree the people between them. Perhaps that is why we get the finer detail.
The Relationship Report deals with everyone in the database and their relationship to one person. That part of the program does not identify so minutely.
Also, the relationship report and the kinship item may have been written by different programmers at different times, anywhere from Roots II, Roots M, Roots III (was there a Roots I?), Roots IV, Roots V, FG, and what was the name of that other program of the month? (grin)
Your 6th cousin is still your 6th cousin even if as a 1/2 cousin. When I find my 1/2 something cousin, I will run both Kinship and Relationship Report.