The Collaborative International Dictionary of English v.0.48:

Batsman \Bats"man\, n.; pl. Batsmen.
   The one who wields the bat in cricket, baseball, etc.; in
   baseball, the batsman is usually called the batter.
   [1913 Webster +PJC] Bat's-wing

The Collaborative International Dictionary of English v.0.48:

Batter \Bat"ter\ (b[a^]t"t[~e]r), n.
   The one who wields the bat in baseball; the one whose turn it
   is at bat; formerly called the batsman.
   [1913 Webster +PJC]

WordNet (r) 3.0 (2006):

batsman
    n 1: (baseball) a ballplayer who is batting [syn: batter,
         hitter, slugger, batsman]