Old English hyll "hill," from Proto-Germanic *hulni- (source also of Middle Dutch hille, Low German hull "hill," Old Norse hallr "stone," Gothic hallus "rock," Old Norse holmr "islet in a bay," Old English holm "rising land, island"), from PIE root *kel- (2) "to be prominent; hill." Formerly including mountains. Figurative phrase over the hill "past one's prime" is first recorded 1950.
In Great Britain heights under 2,000 feet are generally called hills; 'mountain' being confined to the greater elevations of the Lake District, of North Wales, and of the Scottish Highlands; but, in India, ranges of 5,000 and even 10,000 feet are commonly called 'hills,' in contrast with the Himalaya Mountains, many peaks of which rise beyond 20,000 feet. [OED]
The term mountain is very loosely used. It commonly means any unusual elevation. In New England and central New York, elevations of from one to two thousand feet are called hills, but on the plains of Texas, a hill of a few hundred feet is called a mountain. [Ralph S. Tarr, "Elementary Geology," Macmillan, 1903]
Despite the differences in defining mountain systems, Penck (1896), Supan (1911) and Obst (1914) agreed that the distinction between hills, mountains, and mountain systems according to areal extent or height is not a suitable classification. ["Geographic Information Science and Mountain Geomorphology," 2004]