Not all psychopaths kill people, that is a common misconception.
Indeed, the average real-world psychopath is not a murderer. If all or most psychopaths kill people, and psychopathy has an estimated prevalence of 1% in the general population, then it follows that roughly 1% of the general population has murdered somebody. I'm incredulous, to say the least.
However, while it's obvious enough that all or even most psychopaths are not murderers, what may be less obvious is that all or even most murderers are not psychopaths.
It is a personality type. They become killers later when they develop and obsession or feel it will help them achieve their goals.
This seems like a typical quixotic and Hollywood-esque type notion of psychopathy, in my opinion. A psychopath, as you appear to suggest, could never—or almost never; or, as a whole and taken as an average, are at least closer to never than ever relative to the hoi polloi—of committing an unplanned, senseless, stupid, impetuous, and/or sloppily-executed murder that furthered no objectives nor fulfilled any obsessions.
Moreover, while I think it is erroneous to suppose that psychopaths' murders are more likely to have been motivated by cold, calculated, and considered thought than non-psychopaths' murders, there's a paucity of evidence to support the idea that psychopaths are more likely to be motivated to do anything out of cold, calculated, and considered thought.
In fact, the only evidence I've come across with at least a soupçon of solidity makes the opposite suggestion: that the quintessential psychopath is less likely to act out of premeditation and forethought than average.
The average psychopath may not be a murderer, but he—and it is virtually always a he when the person in question is psychopathic, narcissistic or sadistic. (But, to be fair, this also applies to people who are avaricious, power-hungry, eager for success, demanding, or assertive, which is why it's a cultural universal, if not nearly a mammalian universal, for a "he" to be more likely to hold a powerful or propitious social, economic, or political position than a "she", contrary to popular bullshit, crackpot "patriarchy" conspiracy theories)—also isn't a CEO, lawyer, politician, banker, academic, wunderkind with a genius-level IQ , or even employed or employable, for that matter.
A sociopath is someone who was brought up in a demented childhood where they never developed empathy during their youngest years. If it happens early enough it becomes them and is not reversible. Psychopaths were born that way. Many of our leaders have these traits combined with discipline and intelligence so that they seem like exemplary members of the community.
This too seems an odd and unfounded thing to say. If sociopathy is predominantly acquired and psychopathy is predominantly congenital, how does one distinguish the genetic psychopath who grew up in a broken and abusive home from the environmental sociopath?
When deciding whether someone is a sociopath or a psychopath, does one simply examine their childhood and count the number of productivist-pleasing and capitalistic traits they have? Or is there some less egregious and unscientific metric used?