One is stating your blood relationship to him, while the other is stating your connection to him.
Blood relations are literally that - how you genetically relate to that person through what kind of relationship. You can also find a common ancestor if you share that type of relationship.
However, a connection takes the shortest path to a connection through marriages, adoptions, and any other legal relationship to demonstrate how we're "connected" (not necessarily "related").
So I am 1 degree from my wife. But I probably won't show a common ancestor (hopefully) unless it's very far back. So I won't be related in a cousin relationship with her. But as I build my tree, I might encounter someone who is 3-5 degrees from me, who isn't a direct part of my close relationship bloodlines, whom I'm related to through some very distant ancestor. In that case, I'd have a relationship like you describe. 16th cousins 3 times removed (16c3r) and 15 degrees from me.
Hope that helps explain it.