They are both claims on future production, exactly as I said. If the future generation produces 50% less, then there will be 50% less for retirees to consume. It does not matter whether retirement is financed with social security or private savings, there will just be 50% less in both cases.
In neither case do claims on future production "help the business grow". Capital markets price claims, they never fund them, so at best you can say that correct pricing of claims helps allocate investment more efficiently, but that only requires marginal participation in capital markets in order to set prices.
So while capital markets play an important role in setting relative prices of investments, and thus of allocating money away from lower return and toward higher return investments, they play no role in absolute quantity of investment made. For that, just as loans create deposits, so investments create savings - not the other way around. If you are a farmer deciding to buy a new tractor, I guarantee you that you will never be waiting for someone to skip a meal and save in order for you to be able to finance the purchase of your tractor. Rather, an increase demand for consumption goods is required to increase investment and make the bank approve your tractor loan. That tractor investment is never funded by individuals choosing to "save". Rather, the purchase of the tractor is what causes aggregate savings to go up ex post, and whether pensions are funded with transfers or with capital markets has no bearing on whether it makes financial sense for you to take out the tractor loan and thus on aggregate savings.