The concept of a "gunslinger" is almost entirely a Hollywood creation. In fact, the word "gunslinger" was coined in films. During the 19th century these types of men were usually referred to as gunmen.
While the infamous face off scenario did happen they were extremely rare. There was nothing romantic about a gun fight. Movies use them to depict the classic good vs. evil climatic battle but reality is a little less feel-good. Consider: most frontier men carried weapons for protection and there wasn't much of a law presence in many small towns. So it was easy for petty rivalries to escalate and get out of hand after a few drinks or a bad game of poker.
A gun fight usually consisted of one man drawing first and the other returning fire. Usually both of them would dive for cover in the process and it was not at all uncommon for bystanders to get killed since multiple rounds were being fired.
Some men did acquire reputations as gunmen. What this really meant was they had been in several gunfights and lived to tell the tale. If they were the ones to start a fight it also probably meant they were a little off their nut. Not many sane individuals would choose to start a gun fight for fun.