UK Population
1881 = ~35 million, 2001 = ~52million, 
     Census Count
Name         1881            2002 (Est) 
Vines          938             1440
Vine          2612             4175
Viner           942             1480
Viney         1043             1760
 

Distribution of these names throughout the counties in the 1881 census is seen here at these links, with speculation on their origins:
Vines
Concentrated in northern Wiltshire and Gloucestershire since before 1600s, perhaps descended from Anglo Saxons of north western part of kingdom of Wessex. Malmesbury, where there was a large and influential abbey in the time of surname origins, is central to the Wilts/Glos Vines of records and the present day; the name might have arisen from association with the abbey and its vineyards. Grittenham
There is also a lesser concentration of Vines centred on Leicestershire and Nottinghamshire; these may be related to the Wilts/Glos families, or perhaps descended from a separate immigrant line during the reformation or earlier. 
Sparse numbers only along the English Channel coast may be a pointer to no connection with the Vine family.

Vine
Most of this name were distributed along the south coast and up the east coast of England. The large number in Sussex and the other channel counties point to their probable origin in France. Possibly derived from Vigne or de Vigne. There are virtually none in Wiltshire and Glos. and there is little overlap of areas with the Vines name. Connection between the two names seems unlikely. 

Viner
Somerset had the densest population of Viners which extended through the south west counties towards Surrey, and only a light sprinkling along the south coast. A very large area north of Surrey and Middlesex to Linc and Notts had very sparse numbers.

Viney
This name was densest in Hampshire and Wiltshire with lesser numbers in Somerset and Devon. The dozen counties NE of and including Berkshire, to Notts/Linc, Norfolk and Suffolk had very few. Origins may have been a) in the kingdom of Wessex, b) from immigrants through the Bristol Channel coastline, or c) perhaps from wool industry
immigrants heading to settle in the plains of Wiltshire.

US Population
1880 = ~ 50 million, 1990 = ~ 250 million
                Census Count
                         1880                   1990 
Name           All         White       All (Est)
Vines         1223          984          2500
Vine            602           514            600
Viner          142            137            250
Viney          352           158            250