I'd say it's significantly different to take a Providential view, whereby the world was designed in order to facilitate human happiness and this is why self-interest produces moral outcomes, compared to saying saying 'there is no purpose of direction to human society but self-interest produces moral outcomes'.
There are innumerable other considerations which serve to confirm the same conclusion. The happiness of mankind, as well as of all other rational creatures, seems to have been the original purpose intended by the Author of Nature when he brought them into existence. No other end seems worthy of that supreme wisdom and divine benignity which we necessarily ascribe to him; and this opinion, which we are led to by the abstract consideration of his infinite perfections, is still more confirmed by the examination of the works of Nature, which seem all intended to promote happiness, and to guard against misery. But, by acting according to the dictates of our moral faculties, we necessarily pursue the most effectual means for promoting the happiness of mankind, and may therefore be said, in some sense, to co-operate with the Deity, and to advance, as far as in our power, the plan of providence. By acting otherwise, on the contrary, we seem to obstruct, in some measure, the scheme which the Author of Nature has established for the happiness and perfection of the world, and to declare ourselves, if I may say so, in some measure the enemies of God. Hence we are naturally encouraged to hope for his extraordinary favour and reward in the one case, and to dread his vengeance and punishment in the other. A. Smith - Theory of Moral Sentiments
Also Smith did assume an essential goodness to human nature that would promote altruism. People would behave virtuously and this would help balance the system. So there was less need to purposely balance the system through calculated actions and human virtue would lead to charity and restraint.
Again this is based on a Providential view of human society.