What are the reasons/functions behind the different drug triggering receptors in the brain?

I am not real clear about what you are asking, but I will share these thoughts with you.

All cells in the body, including the various types of cells in the brain, have receptors on their cell membranes.  These receptors function as sensors for the cell.  Different receptor types "sense" and respond to the binding of different types of molecules in the cell's environment.

Receptors can sense and respond to both Endogenous molecules (molecules that naturally occur in the body) and Exogenous molecules (molecules that enter the body through the gut, skin, lungs, etc.).  Exogenous molecules would include drugs.

Drugs bind to and activate (or inactivate) receptors that are already present in the brain cells for other reasons than to respond to drugs.  The drugs are taking advantage of the existing receptors!

The cells of the body need to be able to sense and respond to a large variety of naturally occurring changes in their environment.  Drugs "co-opt" this system to artificially manipulate cellular responses.

Best wishes and good luck.