As an acute physician, I was going to say, it is never the other specialities, but all joking aside, there is no clear cut division.
When I was a student in Germany (quite a while ago) patients with a pneumothorax, would come in under the surgical teams and patients with biliary disease/cholecystitis and even pancreatitis under medicine. In the UK, it is often exactly the other way round, and there are good reasons for both ways.
Conditions can transient between different specialities, it is the specific management that often decides on who looks after them. For example, a patient may come in with trauma, i.e. a fracture neck of femur, which will be operated on by an orthopaedic specialist, may need post-operative care under intensive care and will later require rehabilitation under older people's medicine. Often there will be agreements within a certain hospital who should be looking after which condition, this will preempt frequent complications or expected further management. For example, urosepsis in female patients is often admitted under medicine, whilst in men it will be under the urologists. That is because there is a high chance that structural problems will lead to such conditions in men.
Dr.Immo, when there is an overlap between two specialties, how can I know which specialty is the correct one? For example, in the case of Stasis Dermatitis, some say dermatologist should handle it, others say it is a vascular disease, so a Physician who specializes in vascular disease
that will depend on each individual case and your local setup. In the example that you are giving, whilst it is a vascular disease, a vascular surgeon may not have much to offer, treatment with compression bandages, emollients, weight loss, physical therapy etc. may be suggested and overseen by a dermatologist or even by your family practitioner.
In Germany, this is arranged in the continuing education regulations for physicians (attached). Since we have a federal system, the respective continuing education regulations of its regional medical association are legally binding.