Oh Deimos, whatever shall we do with you...
To answer your question, Fin, the difference is:
An Administrator is someone who (in the case of this forum) is part owner and has a say in the decisions that affect all aspects of this website. The Admin also has unfettered access to all the higher functions and tools that the forum software provides, and can make changes, fixes, create and remove entire sections of the site, etc, and deal with member registration approval.
A Moderator, on the other hand, is charged with ensuring that the forums rules, as set out by the Admins, are being followed, and to enforce them upon occasion when they are broken. A Mod can delete or edit your posts, lock a thread or even delete it, and even ban users if the situation calls for it.
Currently, we have no one that is strictly in the role of Moderator, as myself, Olorin, GuardianWolf, and BladeCollector are all Admins ,but we also perform all the functions of Moderators as well. This was not always so, and each one of us did start out as a Mod, hence the title distinction and the green names that some of you may recall from the past. BC has really been and Admin for a long time, but he liked his green name so much better than gold that he opted to remain listed as a Mod.