From what I understand, in folklore, the word "GHOST" was used to specify the spirit was of a creature of the natural world, and not a demon or some otherwise "otherworldly spirit". So, the spirit of God would not understood to be a "ghost" until after Jesus.
In the bible, "ghost" and "spirit" are both translated from the greek Pneuma: and most people, from what I can tell, use the terms interchangeably with reference to the Spirit of God.