I have been DX with both although it's more a case of ruling out other things since there aren't really tests. Mine started out with Fibro because of the pain but then the fatigue I have is more like CFS in that it's debilitating.
I suspect there is a lot to learn about both diseases but just not enough funding.
What if trials of this life are Your mercies in disguise.
FM/CFS, BP, gastritis, diverticulitis, anxiety/PTSD, adult ADD, hypothyroid, brain lesions, sleep apnea that doesn't respond to a c-pap as far as sleepiness/fatigue goes, insomnia and only sleep in stages 1 and 2 and REM with a tiny bit in 3 and 4.