What are the different types of fiduciaries?

So I've been hearing fiduciary or fiduciary duties or fiduciary responsibility a lot in my classes (and in life) recently. As much as I was aware of the word enough to be able to get the jist of the conversation, I hate when I don't know the exact definition and also some examples to help me comprehend it even better.

From my research it appears a fiduciary duty can exist in many different relationships with each situation requiring different expectations of the fid.

Fiduciary originates from latin meaning "(holding) in trust." It is evident trust is the grounding term. Anyone anywhere can be a fiduciary just by having someone else entrusting him/her.

In all cases, a fiduciary has the duty to act in the best interest of the principal.

Examples:
Beneficiary/Trustee
Broker/Client
Teacher/Student
Business Partnerships (but not Joint Ventures)
Executer/Deceased
Doctor/Patient

The list is never ending.
Now I know.

Also I learned today that the formula for calculating the present value of an annuity in perpetuity is the same formula to calculate the value of real estate using a capitalization rate.

Present Value= Annuity/Discount Rate

Or

Value of RE= Net Operating Income/Cap Rate

WHO KNEW!