The meaningful difference is in the routes into the working in the field of dermatology and trichology.
Dermatology includes the study of skin, hair and nails. In the UK it is accepted that this is mainly done by doctors and nurses. The majority of dermatology practice in the UK involves the skin. Trichology includes the study of hair (and scalp) only.
A consultant dermatologist in the UK is a doctor specialising in dermatology. Consultant dermatologists will have completed at least 5 years of undergraduate training in Medical School, following competitive selection requiring high grade A levels. They will be able to prescribe and like all doctors their practice is regulated tightly.
In the UK, to become a consultant dermatologist (referred to elsewhere in the world as Board certified dermatologist) following the medical degree the doctor will become then complete a two-year foundation programme and then two or three years or more of core training. Successful completion of the training programme means that the doctor’s name can be entered on the Specialist Register of the General Medical Council which regulates all doctors. Entry to the speciality of dermatology is competitive, so some doctors may have additional experience in related areas genitourinary medicine, rheumatology, medical oncology and immunology.
Because of the comprehensiveness of the dermatologist’s training they are able to participate with other medical disciplines in the diagnosis and treatment of all types of hair problems as they may relate to systemic disease e.g. lupus. They are trained to recognise a much wider range of conditions than trichologists. They can take biopsies (skin samples) from the scalp to help diagnose the more challenging hair loss conditions. In addition they are able to prescribe some medications that General Practitioners can’t e.g. Hydroxychloroquine for a hair loss condition called Lichen Planopilaris.
In the UK dermatology is included in the syllabus at medical school where doctors complete their basic training. However a Kings Fund study published in 2013 indicated that the majority of GPs receive less than one week’s training before they qualify.  The study of hair and scalp disorders would have only formed a small part of this. The majority of that training is likely to have taken place in medical school.
 The King’s Fund, How Can Dermatology Services Meet Current And Future Patient Needs While Ensuring That Quality Of Care Is Not Compromised And That Access Is Equitable Across The UK?, 2015. <https://kingsfund.blogs.com/health_management/2015/05/how-can-dermatology-services-meet-current-and-future-patient-needs-while-ensuring-that-quality-of-ca.html>