Yes, the source of stress matters. I don't know a lot about the context of your question but just wanted to add that most companies offer Employee and Family Assistance Programs that covers counseling which can be an effective way of figuring out what to do about the non-work stressors.
That is a genuine concern. Allegedly, HR doesn't get access to that sort of fine-grained medical data. But I'm honestly not even comfortable bringing this sort of thing up to any of my managers I've ever had, despite having a fair amount of trust in them.
