The bookie’s winnings come from the “vigorish.” Las Vegas sportsbooks sell $21 football tickets for $11 each. (They’re paying only 10-11, not even money.) Suppose they sell ten Rams tickets and ten Patriots tickets. They’ve collected 20×$11 = $220 and paid out 10×$21 = $210, for a $10 profit. If their bets are balanced they earn 50¢ per ticket regardless of who wins.
You are correct about the odds, but not quite correct on the rest. In parimutuel betting, the bettors set the odds with the amount of money they put through the betting windows.
Parimutuel betting is best described as “the bettors are wagering among themselves.” Thus, the odds posted on the tote board–which change right up until the race starts–indicate the ratio of money bet on one horse against all the other horses in the race.
The track does not set the odds; those are resolved by the parimutuel system. It is true that the track will post a morning line, which is an educated guess by the track handicapper as to what the final odds will be, but that is all it is–an educated guess. It will have no effect on the actual odds (except, perhaps, as a guide to horseplayers as to which horses merit attention, and which do not).
What the track does is act as a stakeholder, putting all bets into a pool from which it will pay winners. But not before the track takes its fee for acting as stakeholder–this can vary from 17% of every dollar, to 25% depending on the bet and the jurisdiction that has licensed the race meet. So your $2 exactor bet contributes $1.50 to the pool after the track has taken its cut. (Example only; YMMV in your jurisdiction.) But this percentage cut is how the track makes money. In other words, the track doesn’t care who wins; it makes money on most races. There are exceptions when a negative pool occurs, but they are rare.
But I don’t think the OP is referring to parimutuel betting.
Your post is correct, but I was startled to hear mine labeled “not quite correct” since it was intended to provide the identical information, if more tersely. 
If instead of “The track sets the odds so that it wins a constant percentage” I had written “The track sets the odds using the assistance of an arithmetic calculator so that it wins a constant percentage” would you have thought better of my wording?
Note that Vegas sports books attempt to approximately balance their books in real time, and therefore the customers of such a sports book are also, approximately, betting among themselves.
So the idea is a bookie does well when they are good at predicting what people want thereby getting more bets all the while diminishing their risk.
Ok, but the Vegas spread is published in every daily newspaper. Do local bookies change those odds for their audience and if so does that really work to gain more profit? And if they do, we live in the internet age, if my Packers are playing the Lions and some local Detroit bookie is giving the Lions better odds than Vegas, I’ll place the bet with them to their detriment.
There’s different types of “bookie” but most will try to keep their bets balanced by adjusting odds or spread in nearly “real time.” Still, there will be arbitrage opportunities. A Brit enrolled as Doper just to post in a thread (2012 IIRC?) that he had a sure-thing going. IIRC he was betting against Obama’s re-election at the British Betfair site, while betting on Obama at some large U.S. site. You’ll see very different odds at different U.K. books, though I’d guess vigs, fees and tie-up costs will make easy profits hard to come by.
Bookies have access to the 'Net also! In your example (I’ll guess the Detroit bookie would be offering worse odds on the Lions than Vegas offers) wagers may be for sale at different terms in different localities, but you must factor in the cost (and even legality) of placing a long-distance wager.
I’ll admit that your added explanation suffices to flesh the matter out better to everybody participating in the thread. Can we wish each other good luck in handicapping next week’s races at the track of our choice?