Hi Jim,
Administrators refer to Greg and chroot, who mainly look after the technical-side of the site, coding and server management, Greg is also the site owner.
Moderators and Mentors are the same position, as you can probably guess they are tasked with moderating the forums, ensuring that a level of scientific accuracy is maintained and 'run' the site on a daily basis. Mentors have to power to move, lock, edit and delete threads as well as ban individual members. I imagine (although I don't actually know) that the mentors also have a significant say in how the site evolves and I'm sure Greg consults with them on any major decisions.
Science advisors (SA's) are people who have been nominated (and seconded) by either administrators, mentors or current SA's as recognition of demonstrated scientific knowledge and understanding on the forums.
Homework helpers (HH) are those who have been nominated (and seconded) by those groups mentioned above and additionally current HH's as showing a commitment to helping students, usually in the homework forums.
SA's and HH's don't have any specific responsibilities beyond those which they impose on themselves. Although generally, the SA's along with the mentors can participate in the review of submissions to our independent research forum.
I don't think that they are particularly consider 'ranks' here, more as recognitions, or awards. I find that PF operates a far superior system than those forums that award ranks based on post count and/or at the discretion of one or two individuals.
[Edit: Looks like I was beaten to it]
).
*ducks and runs*