Intrusive Thoughts

Wondering about these... how can you clinically say you have intrusive thoughts?

Is it the same as when you think "I wish it would all end" out of the blue? As in you didn't think it yourself, it just came to you but in a voice... sort of? This is hard to explain. I can be sitting there not feeling depressed or not feeling anything really and I will think "I wish I were dead". I will even be somewhat startled by the thought!

But then I will have this back and forth with myself... and something within myself. "But your kids need you" will start it off "Oh they seem pretty happy with your mom, maybe they would enjoy it better if you left them with her?"
"Oh no, mom can't handle them. I don't want to burden her. Besides, they would be devastated if you took your own life."
Other thing inside of me "But not for long. Besides, (son) could go live with his father and (daughter) would probably live with your aunt. She has a nice home and she is really a wonderful, nurturing person"
Me "Oh stop now. Besides, I might go to hell if I off myself. Perhaps I can get into heaven if I don't do it"
Other thing "Maybe. Maybe you are damned. Maybe there is no heaven."

And this can go on and on. It's really quite distressing.

It's not just suicidal talk though, in fact that is in the minority. I will have "conversations" in my mind that emotionally subdue me to the point that I may or may not be upset or completely over it based on how the conversation goes in my head. But it's not always me in the conversation. Sometimes it is other people and they are talking about me. That I can at least recognize as paranoia.

So, are these what intrusive thoughts are?

Let me add, I have music in my mind most of the time. This makes it hard to concentrate. Also distressing. Just thought I would add that.