Sentence:  The difference is that wizard mode is a SUBSET of <WSD>god mode</WSD>.  For example, both wizard and <WSD>god mode</WSD> let you "teleport", but only <WSD>GOD mode</WSD> allows you to "allocate treasures" or "create object". 
Meaning of the word marked with <WSD> tags:  A mode of play in (mostly) roguelike games, allowing the player to create objects on demand, to be resurrected in the case of death, etc.