Sure, it's an acronym that technically means the same thing... however, in the world of Diablo, PK and Duel are very different.
Duel = mutually agree to hostile and attempt to kill each other. Characters are set-up for PvP. They have gear and charms that boost dmg and life.... or res and absorbs... etc... depending on who you're trying to kill. In theory, it's close to a fair fight.
PK = a PvP style character like above enters a PvM partied game, where other characters are only set-up to kill monsters (huge difference in gear/charms, even skills sometimes). PvM set-ups hardly ever stand a chance vs a PvP set-up, but on top of this, the PvP character will unleash a surprise hostile & kill during an awkward situation.
This would be like a man training in boxing for a few months, only to go out and knock down an old woman for her purse. Except he doesn't even get the purse. Why doesn't he step in the ring and fight another man? Oh, because he's a coward.
Ever been in a full dueling game? It's actually quite entertaining with people talkin' trash and tryin' all sorts of methods to get the kill. However, take note of the guy that keeps dying and is bothered by it. Check the trade channel about a week later and you'll see people crying about how that guy just pk'ed them. LOLZ What a loser.
If we're talkin' softcore... no big deal really. All you lose if what? Some gold and xp? But if hardcore... ughh. You character gone and for what? The PK'er gets nothin' but an ear, which NO ONE cares about. It's simply a malicious act. In fact, if you PK a high-lvl character that someone has been working on for a long time, that person might actually quit D2.
And of what I've seen of Black Moon... all their "PK skillz" are based on TPPK hax! OMG! That's even more pathetic.
Anyway, if the OP was referring to starting a dueling clan... cool, go for it. But if you meant PK, as I've described, then I'd have to inform you that you're gay.