In our country it tends to be CFS if diagnosed by a primary care physician and FM if diagnosed by a rheumatologist.
The symptom list is identical. From a patient point of view CFS is usually characterised by fatigue, and FM by pain though we tend to have a selection of the same symptoms.
Yes, they have a symptom picture for a basket diagnosis. No etiology there for no means to a cure.
Many cases of Fibro in the US are turning out to be lyme. There is only one sure fire way to diagnose lyme and that is with a dark field live blood analysis microscope. You can see the cysts and the spirochetes.. I've seen the photos from an electron dark field scope also.