Creating wealth is not a zero-sum game. So your phrase: "I was always under the impression it basically just gets shifted around" is wrong.
Basic economics, man.
The extension of this is that if you've accumulated great wealth (through the market, rather than through dictatorship or government) then you have also generated great wealth for your business customers or clients. But that wealth will be more spread out.
The fact that wealth is not a zero-sum game doesn't mean that your second claim follows: it is not the case that all transactions are positive-sum. Not all accumulation of wealth produces a multiplier; it's possible to make a fortune by siphoning off money with no net creation of wealth, or even by net destroying some.
Every bank loan is new money in, at minimum, the form of an interest charge (but more often on some or all of the principal too). The principal+interest paid to the bank is more than the principal alone, even in the simplest case. In either case, however, the bank has "made" money (but not wealth or value) and devalued (inflated) the paper currency in circulation. (You, however, are expected to make value with the capacity to transact that has been loaned to you). In the case of almost everyone else however, I agree: people are largely competing for the pre-existing numbers. But banks get to make them up, and that function is independent of the printing of currency. The actual currency is just printed as needed to facilitate trade, satisfying debts, and hopefully the creation of wealth; hopefully the wealth created is enough to counter the wealth removed, because otherwise there's lots of vacuums running around sucking up value. Oddly, most modern countries accumulate interest-bearing public debt (inflation and interest), employing banks as lenders, instead of just printing the money (currency) to spend on worthwhile projects and to remove from circulation when they're done.
Basic economics, man.
The extension of this is that if you've accumulated great wealth (through the market, rather than through dictatorship or government) then you have also generated great wealth for your business customers or clients. But that wealth will be more spread out.