To be honest, what you describe is classic Sleep Apnoea symptoms (although I must stress I'm no doctor). It's exactly how I felt before I was diagnosed.....constantly fatigued and no sensation of that dozy, sleep feeling. I think it's just peoples way of describing how they feel.
Either way, if you feel completely fatigued all day long, if you suffer from headaches and aching legs and if you feel like just giving up, you almost certainly need to get sorted
And you're right, I used to find it hard to switch off at night, especially knowing that I'd wake up the next morning feeling just as bad, if not worse.
Keep hanging in there. Once you get the treatment, your world will change.