Hi.
I will partly enlighten you, because I only parly know the answer!!
When you are building a skeleton, and you parent one bone to the other, the bones get connected. When you use a parent constraint, the bones act like they are parented but they remain two seperate chains.
And...I think there might be a little more to it than that. Oh yeah, look at the heirchy in the hypergraph when you do the two. One puts the child node underneath the parent while the other leaves it where ever it normally is.
(Anyone correct me if I'm wrong on this next part)
When you parent constraint stuff it's the same as doing a point constraint + a orient constraint, or conecting the values in the connection editor, I soppose. It makes one objects translates and rotates equal to the other's. I think it leaves the scales alone, but I'm not sure about that, I don't have maya in front of me right this second to check it out.
Did you check the index in the maya help files?? I've found that to be often helpful.