I'm not a psych major or anything so I'm not qualified to speak with authority, but I personally make a distinction between "unwanted thoughts" and "what a person actually wants", but I'm not saying there's a specific clear-cut distinction. But I do believe that there is a distinction.
Example: I've found myself having persistents thoughts about wanting to die while I'm in bed waiting to fall asleep, but eventually I always realize that no, I don't actually want to die because despite the shitty parts, I do find fulfilment in living and being alive. But that doesn't make the thoughts stop coming at night. This is just my subjective view on it, but yeah.