Saw Shane and Lara briefly at Starbucks before I headed home from the meeting. We were sitting around and I mentioned that I though Plutocracy meant "rule by the wealthy", while Shane said that it was Oligarchy that meant "rule by the wealthy".

Plutocracy does means rule by the wealthy.

while

Oligarchy seems to mean rule by a small number of people (the "elites"), where those people may be rich, but might just as readily hold military power.