The distinction between producer's surplus and profit.?

Since Producer's surplus is the difference between the price of the good and marginal cost/marginal "profit" (area between the price and supply curve), it intuitively indicate it's the net profit, but then we know that in a competitive market, the producer's profit is 0. How would you reconcile the two concept. (my guess is that the producer's surplus is merely the accounting profit which does not take into account implicit cost, while when we talk about 0 profit in a competitive market, we ume it's the ECONOMIC profit which include both explicit and implicit cost.) tell me if i am right.