I never said mediate/mediator but intercede/intercessor. The difference being in the primary meaning of each word, which I meant to convey in my usage (the word intercede also has a secondary meaning which is a synonym to mediate, but I did not intend to use the word that way).
Here are the primary meanings:
Intercede (v.intr.): To plead on another's behalf.
Mediate (v.intr.): To work with two or more disputants in order to bring about an agreement, settlement, or compromise.
Jesus is not the only intercessor to God (though he is the greatest) in the primary meaning of the word. But only Jesus can mediate to reconcile us with God. I hope this clears up what I wrote.