Sleep apnea at the surface looks like CFS since you aren't consciously aware that you stop breathing in your sleep but still feel tired all of the time when you wake up in the morning.
Lots of things look like CFS on the surface, including depression. I expect there will turn out to be many distinct physical diseases responsible for what we call CFS, as well as simply depression. I remember first reading about CFS over a decade ago when most of the information available on the internet was on sufferers' blogs and forums and being struck by the prejudice against mental illness. There were a lot of comments to the effect that, "The doctors said it was all in my head, but then I learned that Chronic Fatigue Syndrome is a real disease! It totally changed my life knowing that I was sick and not crazy! I don't have to hate myself anymore." A lot of anger was directed at doctors who suggested psychological explanations. Even saying, "We can't find any physical cause, so maybe you should talk to a psychologist as well," (which sounds like a reasonable suggestion to me) was treated as a disrespectful, belittling, arrogant, and sexist. Which I suppose it was in many cases — there's certainly enough prejudice to go around. But for me as someone seeing a therapist for depression it certainly made me look at the people around me differently, having that unguarded glimpse into the revulsion that some people feel.
Only on the very surface. Sleep apnea is relatively easy to test for. ME/CFS sufferers experience a kind of fatigue that is distinctly different from that caused by sleep deprivation. Look up PEM / PENE: