The term "ball carrier" can be used to describe a player who carries a ball during a game. However, there are several synonyms that can be used interchangeably to describe this player. For instance, a ball carrier can also be referred to as a runner, a ball handler, a carrier, a ball carrier back, or simply a back. In football, the term rusher can also be used to describe a player who carries the ball. Additionally, in rugby, the player who carries the ball is commonly referred to as a ball carrier or simply as a runner. Regardless of the sport or competition, these synonyms can be useful to add variety and diversity to your writing.