Traditionally these alternatives capture the three primary modes -- cardinal, fixed, and mutable; or deontic, alethic, and optative (more commonly volative, but I prefer the Greek word); or symbolic, realistic, and imaginal; or 'should/may', 'could/must' and 'would/might'... These also coincide with some personality theorists division of people into Jungian types of SJ, SP and N, which splits the population roughly in thirds.
The first option is fixed or alethic or realistic or 'could/must' -- it is a matter of survival or advantage in material reality to comply. 'One could do better by...'.
The second option is cardinal or deontic or symbolic or 'should/may', it is a matter of social convention, duty or symbolic obeisance to comply. 'One really should...'.
The third option is mutable or volative or imaginal or 'would/might', there is no reason to comply other than the whim of those in the position to command. If he is truly justified, we somehow trust the vision and obey. 'His majesty would rather that...'.
The last case is more complex, because if the leadership is not truly justified, obviously it then becomes a fixed position to comply when the commander is free to use force or a cardinal position when he is in his position for traditional, religious or political reasons. But the rule itself, and the argument for it, is mutable.
Another way of looking at option 3 is that it represents a more evolved, less pure version of the mutable principle, a relativistic posture, or a doxastic mode, where I work from belief. Instead of responding directly to the idealistic world, I comply, am willing to be coerced, or allow/cause others to be, when the directions resonate with my own ideals, in that they either excite or conform with my imagination.
Then I find an authority justified when its ideas are consonant with my ideas, either purely when I subjectively feel they are likely to be right, or when those ideas have been shaped by other modes, but are now past consideration, and have become guiding ideals that shape my imagination. (Basically, this is intuitive behavior that is not rootless or flighty, but instead firmly attached to what one is passionate about, to the point that logic is not what would change ones mind.)
Since alchemy, modal logic, psychoanalysis, philology, etc. have different ways of putting the same thing over and over, I would say there is no 'standard' set of terms. But the set of deontic, alethic, or optitive/doxastic modality are most likely understood by a lot of philosophers.