But can't certain things fill both definitions? Two people together can be a pair because they are both people but they can also be a couple because they different but complementary individuals. Words also have multiple definitions and I think you tried to limits these words a bit too much. I would tend to agree more with tj1983. A pair often refers to a matching, or more intimate relationship, that couple. "A pair of friends go out" indicates a closer bond than "a couple of friends go out" but the objects themselves are the same in both cases.
I think that a pair of friends go out implies 2 friends while a couple of friends implies more than 2, not anything about the relationship itself.
In terms of a relationship, I think pair and couple refer to their verb forms. A pair was paired off, a coupled was coupled together.