When you decide to buy a stock, or you're ready to sell, you may debate whether you're making the right decision. You may wonder what the transaction will cost you. But you are unlikely to waste much time worrying about whether the right stock will be traded or if your account will be credited (or debited) accurately.
Your confidence is well founded, especially if you consider that more than 3 billion shares change ownership on an average day. Of course, part of the reason the transfer works so well is that the shares don't literally change hands.
That's because a system of clearing and settlement is a crucial part of the path of a stock trade.