What is the difference between an oligarchy and a theocracy?

An oligarchy is rule and governance by the rich and powerful, usually the business class but sometimes the elite who inherited money, land, mineral rights and/or livestock, etc. A theocracy is rule by spiritual leaders. Both rely on the masses embracing supportive belief systems.

Rebellion always occurs if rule isn't just. Neither belief system lasts or works well. [See Discussion on this line]