The people who worked for the numbers racket were called number runners. They collected the bets from the gamblers and delivered the payoff when the gamblers won. Sometimes, these number runners were said to be "running numbers."
the winning numbers were often determined by the final digits of the winning payoff results of horse races. It is also true that when you compare the numbers game which was an illegal lottery to today's legal state controlled lottery, it did offer higher payoffs.
But, the numbers runners were not bookies. A bookie is a person who takes illegal bets on horse racing or sporting events. Contrairy to what the Wikipedia says, these two professions were not combined because the numbers game and sports betting were usually controlled by different people. Also the bookies took bigger bets and looked down on the number runners who survived by taking many small bets; hence the terms "numbers runner" and "book maker" refer to different people.