Yes wishing you would die but not wanting to kill yourself is still a suicidal thought.
Although you may not want to actually kill yourself it can still be a suicidal thought to want to die.
There's been times where I've wanted to die and get it over with but I could not actually go through with killing myself.
I've always been told that things will eventually get better even though it seems like they will not.
If you do die or kill yourself then things in your actual life cannot get really better.
I don't believe in the afterlife so I would rather be alive and find out if things do eventually get better which I believe they will overtime.
But if I die then things cannot really get better although I would not be alive to experience life.
Life is already short anyway so there's no need to speed up the death as it will come soon anyway.