That's not to say, of course, that there aren't sadistic psychopaths, but psychopaths aren't necessarily sadistic.
Extreme sadism — taking pleasure in others' pain — actually gets its own personality disorder, aptly named sadistic personality disorder.
But sadism and psychopathy are characteristics that can be separated from one another, even in seemingly normal people. Some have suggested that the dark personality triad — narcissism, psychopathy, and Machianvellianism (manipulativeness) — could use the addition of sadism and become a tetrad.
If a psychopath is motivated by sadism, like the infamous Vampire of Dusseldorf, Peter Kurten, then you'll get a sadistic, murdering psychopath.
But take Anton Chigurh, the character played by Javier Bardem in the movie adaptation of "No Country for Old Men." He's a hit man sent to track down a missing satchel of drug money. He kills people (lots and lots of people) to fulfill his purpose, but it's not for pleasure.
If you've ever heard a villain tell the hero, "I'm about to torture you, but I take no pleasure in it," you're familiar with this idea. A full-blown psychopath will use any means, including violence, to get to the end — but that doesn't mean they're a sadist.