Although some symptoms of fibromyalgia and joint hypermobility / Hypermobile Ehlers-Danlos Syndrome (HEDS) appear to be the same, their aetiologies are very different. Unlike fibromyalgia, HEDS is congenital.
Ehlers-Danlos Support UK
A paper by Baeza-Velasco, Sinibaldi and Castori (2018) discusses possible reasons for the association between ADHD and joint hypermobility, which I will summarise some of their suggestions here. I'll use the abbreviation 'GJH' (Generalised Joint Hypermobility).
People with GJH often have 'impaired proprioception' which affects their balance, posture and coordination. 'Maintaining motor competencies' (p.169) may overload their executive functions and attention, which generates ADHD.
Musculoskeletal pain (in both GJH and fibromyalgia) affects a person's attention, concentration skills, and other cognitive functions.
GJH and fibromyalgia are often associated with dysautonomia, which is also linked to attention and cognitive issues.
ADHD and GJH are different effects of the same genes, which affect connective tissue and the brain.
The paper also explains that there are 13 different types of Ehlers-Danlos syndrome, and the hypermobile type is the only one for which a genetic mutation has not been found.
Reference:
Baeza-Velasco, C., Sinibaldi, L. and Castori, M. (2018) ‘Attention-deficit/hyperactivity disorder, joint hypermobility-related disorders and pain: expanding body-mind connections to the developmental age’, ADHD Attention Deficit and Hyperactivity Disorders, vol. 10, no. 3, pp. 163–175 [Online]. DOI: 10.1007/s12402-018-0252-2.