Figuring out suicidal thoughts?

I understand that a lot of people have suicidal thoughts. I try to be rational about dealing with mine, but I was wondering if anyone has ever felt they like have 2 different people, or 2 different trains of thought and reasoning inside their head when it comes to suicide? There's 1 person that has become so calm and peaceful, and even quietly reassuring about killing myself. That person is not afraid of life or death and is clear headed and relaxed and soothing. I've only had 1 suicide attempt, and it was feeble, but that was the person inside my head at that moment, and I was not panicking. I was very calm and felt very in control. The other person is the panicked person. I try to talk and reason with the calm, suicidal one. It's like I beg with myself, I plead with myself, I cry about it and literally say the words "Please stop hurting yourself" inside my head. I don't want to die. I am terrified of this part of me that is so relaxed and drawn to suicide. So maybe that means I'm not even suicidal? But are thoughts like that normal then? Do other people have them?