A bookmaker, or bookie, is the individual responsible for taking bets. In modern parlance, a bookie is the illegal version of a bookmaker, who typically works for a sanctioned, legal sports gambling operation such as a casino. They are however synonyms, and can be used interchangeably.
A bookmaker works in the sportsbook, and is the individual who accepts the action. He/She picks the favorite and the underdog, and decides on point totals for people to bet on as well (or has a handicapper do it for them). The calculations which determine what the line should be differ from bookie to bookie, and often depend on the status of the sportsbook they work for. The goal is to always create a betting line that encourages half of those wagering to choose the favorite, and half to choose the underdog. This maximizes the profit because the bookmaker will always win the maximum amount of money. If a large proportion of the bets come in on one side, a bookmaker will often shift the line to compensate and encourage bets in the other direction.