If a person feels compelled to kill other people, and acts upon this (a serial killer), is s/he mentally ill?

i'm studying mental health and i am trying to understand the difference between being driven by delusions to kill someone, and just having a personality trait (not a mental illness) that drives someone to kill other people. it is important for courts of law to make this distinction when deciding whether to send a murderer to hospital or to jail. harold shipman, for example was never deemed to be mentally ill. but there must have been some unusual belief system there for him to think it was ok to do what he did.