It would help if we knew the mechanism by which "stun" stuns and "vaporize" vaporizes. Is it the same thing? That is, does "stun" shake your atoms enough to upset your body chemistry, while "kill" shakes them till they fall apart? Or does "stun" deliver an electrostatic shock effect of some sort, while "vaporize" delivers nothing but causes the target atoms to phase to a different realm? Etc.
From the two-barrel guns of STXI and ST:ID, and the three-barrel guns of "The Cage", "Where No Man", "Man Trap" and "What Are Little Girls Made Of?", we might deduce that stun beams are generated by completely different machinery and thus possibly based on completely different phenomena from the kill ones. It is only later in TOS that guns are built that integrate the two barrels more closely (the ring and the spike), and in ST:TMP and onwards that the technology gets clever enough to only require one barrel (actually, in ST:TMP and ST2, there are four!).
Does stun hurt? If so, people suffer in silence and only groan afterwards, as the effect wears out (quickly in some cases such as "Man Trap", more slowly in others). But suffering in silence is a very plausible outcome when your body is being stunned - it simply becomes impossible to scream because your muscles fail you!
Does kill hurt? Devil's advocate might say that it doesn't - and when certain victims cry out, it's out of fear and rage rather than pain. Falling from a skyscraper doesn't hurt, either, but people still scream...