A game of Warhammer: the Old World is broken down into a number of 'rounds'. During each round, each player takes one complete 'turn', so that by the end of the game both players will have played the same number of turns. Players alternate taking turns until the battle is over.
Whenever a rule refers to a 'turn', it means one player's turn. If a rule encapsulates both player's turns, it will specifically state 'round'.