Suicidal thoughts are pervasive thoughts about death, dying, or killing oneself - not to act on it.
Suicidal threats would be if they had thought out a plan to die by suicide.
Non-Suicidal Self Injury refers to any current self-harm used as a negative coping skill - i.e., cutting (with blades, paper clips, other sharp objects), excessive drinking, excessive drug use - without the intent to kill oneself.