“A halfback, sometimes referred to as a tailback[1], is an offensive position in American football, which lines up in the backfield[2] and generally is responsible for carrying the ball on run plays.[3]”
Right. As opposed to a fullback who will line up in front of the halfback in an I-formation and be a lead blocker. But fullbacks can carry the ball and be receivers just like halfbacks.
Typically the fullback is the bigger running back and does most of the blocking duties and the halfback is smaller and quicker. The fullback might get the ball more often in short yardage situations. Larry Csonka was outstanding at the short game.