[DeucesUp]

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It's all semantics. In the end it all averages out though, and the winner and loser each pay half the juice.

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This is really the correct answer. The system is set up such that the book takes in more more than they have to pay out hence everyone who's betting is paying vig.

I'll give one more way of looking at it which I think shows that both winners and losers pay vig:

Consider instead a betting exchange with no fees. When a bet is agreed upon, there is no vig - 100% of the money wagered goes to the winner. Now one person on this exchange is offering to take bets on Sea+4-105 and another is offering bets on Pitt-4-105. The "market" is giving a fair value of this game of Sea+4+100 the midpoint between these offers. These two offers that are out there haven't been matched up because of the "bid-ask spread" between these two numbers, neither is willing to lay even odds on their bet they both want to get back +105.

Now if you want to take one of these bets - it doesn't matter which one - you have to "jump across" the bid-ask-spread and lay -105. Clearly from a trading point of view, you've taken the worst of it. You've conceded the even odds and agreed to pay -105 odds which is essentially vig. In this model, it is always THE BUYER who is agreeing to take odds worse than the fair market value. Note that it doesn't matter whether the bet wins or looses, the buyer paid his "vig" when he accepted odds worse than what the market was valuing the game at.

In the case of the sportsbook, the bettor is always "the buyer" and the sportsbook is always "the seller". The sportsbook is offering bets on both sides but the odds offered on both bets are decreased from the fair price, generally making you lay -110 when the fair price is +100. You pay the vig when you accept the bet at decreased odds, it doesn't matter whether the bet wins or looses.