Hearts are heart-shaped too... Maybe you guys just have a different name for them. Nobodies are formed when Heartless attack someone, defeat them, and take their heart for the darkness, but the victim's strong enough to linger without it. The heart decays into another Heartless, and the body stays as a Nobody. Emotionless and empty.

[That's a combination of the explanations he was given and first-hand observation, and it's not exactly wrong... It's just also not the full story.]