How does cfs relate to other illnesses such as fibromyalgia, multiple chemical sensitivities, gulf war syndrome, neurally mediated hypotension, Lyme disease, and candida?

Simply put... The underlying theme describes a constellation of signs and symptoms that we have absolutely no clear, concise idea how it biologically works, how to effectively treat it, and how to address its neuro-psychiatric effects, unfortunately, it is this ambiguity that is being exploited by some quacks, to spread misinformation about each of the diagnoses mentioned (and it's not exhaustive).
Similar symptoms but. Many people with cfs have symptoms similar to the conditions you mention, but by definition someone with cfs has severe fatigue with no other known causative illnesses. Thus, if someone has lyme, by definition they do not have cfs, as lyme is the cause of their symptoms. However, many with a diagnosis of cfs may have underlying problems like lyme or candida that have not been properly diagnosed.
Symptoms! Fatigue is a symptom. Cfs is given as a diagnosis when no cause has been found. However, fatigue, like any other symptom, always has a cause. If the cause hasn't been found, then you just haven't looked in the right place(s) yet. The main methods currently used for diagnosis (blood work, imaging studies, etc.) don't always show the cause, and other methods then need to be used.