In Britain, there is no question as to the dividing line. That is because the Ordnance Survey (OS) are the recognised map-makers for the country. They use whatever the local name is to describe high lands. For example, if something had always been called "the Black Mountain" by locals, then that's what they'll call it.
Other than that, throughout England, Wales and Ireland, the OS stipulate that those above 2,000 feet qualify as �mountains'. Some people maintain, however, that a mountain must have a specific �peak'; on that basis, Kinder Scout - the highest area of Derbyshire's Peak District at 2,087 feet - is just moorland rather than mountain, despite the area's name!
In Scotland, there are various names for different mountain-heights...2,000 - 2,499 feet are Grahams, 2,500 - 2,999 feet are Corbetts and 3000 feet plus are Munros. The last of these is now also applied to mountains in England, Wales and Ireland.