I sometimes get fleeting thoughts about hurting strangers, though they aren't as "loud" as my thoughts of self-harm. I would never, ever lay a finger on anyone else. I'm a peaceful person. (If thoughts of hurting others disturb you, chances are good that you are, too.)
From what I understand, everybody thinks about doing horrible things once in a while. It might be that people with mental illness have greater difficulty dismissing these bad thoughts because they're inclined to dwell on things/lose themselves inside their own heads/get stuck in thought loops.