When I was in school in the 1940's I came across the assertion in a geography text book, that 'Clift' was an occupational name connected with coal mining. A 'Clift' was the person in charge of a 'heading', i.e. a branch tunnel into the coal from which the coal was actually being cut. If this is so, then it follows that there should be a predominance of Clifts in coal mining areas and that the name is of no great antiquity. It's possible that Cliff and Clift, though similar, have quite different origins.