Both lose when their clients win.
Both win when their clients lose.
Both profit from a spread (the vigorish for the bookmaker, and the bid-ask spread for the forex broker).
In response to edits
It sounds like you're asking how companies make money converting say US Dollars to Canadian dollars. It's simple, they charge commission.
If you want to buy Canadian dollars with US Dollars on OANDA you just give them money, and they find someone willing to sell you Canadian dollars. And they take their cut as a commission.
The spread shouldn't matter. You want to buy something with your money - don't overcomplicate it. If you're trading in raw currency it's essentially the same as a stock.
The reason your question has generated so much confusion is there is a large currency futures market. Most of the time when people are investing in a currency they actually are investing via a future.
Here is where you're wrong. The broker charges a commission. The commission may be based on the spread, but he doesn't profit from the spread itself, but profits from people looking to trade currency. The last sentence is key - he does not profit from the spread itself (but it may be used to calculate the commission).
In any market, you own a product. The product may be a piece of paper, but you are buying and selling a piece of paper. In order to determine the value of your product (or piece of paper), you have to go to the open market and try to sell it. A broker is a middle man to help you buy and sell your shares (pieces of paper).
A bookie makes odds and sells them. He essentially selling you fake money that's only spendable at his place if you win. He also sells you a piece of paper, but it's a bit different.
You don't own anything. You don't own a piece of the team/horse/whatever, you own a piece of paper that is only good with 1 guy if you win.
Because the paper is only good with one guy, there is no open market. Sure you can find a bookie with better odds, but once you buy in that's it.
Because there is no open market, the bookie makes his money by making good odds, not by commission. The bookie loses when too many people bet one way and win. He's counting on fools on both sides of the bet to profit. The bookie isn't a middle man.
Bookmaking isn't that hard, and the state wants everyone to play the lotto. Bookies are taking the stupid tax away from the state and putting it in their pockets.
Ok - so #4 isn't explicitly how gambling is different from trading, but I bet not many Forex brokers blow 1k a year on lotto tickets, which is what the average American does. The government can't easily corner the Forex market, so it uses an old stand-by to profit - taxes!