Traditionally, ninja were experts in the arts of stealth and deception over using brute force or open combat, using distractions to confuse their enemies and sneaking past them to perform assassinations. In addition, their swords and other equipment were known for being low quality. This was a deliberate choice on their part - using cheap equipment meant they wouldn't hesitate if they had to abandon it. Female practitioners of the art were known as kunoichi, and specialized in using poisons, disguises, and the use of their gender as an advantage over men, only using their close-combat skills if they were caught.
On the other hand, the video game ninja, regardless of gender, is typically seen as an impossibly skilled martial artist who specializes in direct assault, usually with a specific magically-enhanced katana that's been in their family for generations. Game ninjas are occasionally associated with misdirection and confusion attacks, such as smoke balls that obscure an enemy's view. Also, many game ninjas possess some form of "ninja magic", such as Ryu Hayabusa's "ninpo" spells.
Some game ninja, most notably the characters found in the Tenchu series, do rely on stealth, though they seem to be in the minority.
Notable Video Game Ninja