In the iTunes Store, you have the ability to redownload an app you already purchased, which is useful if you've lost the backup copies on all your devices. But it's not immediately obvious to everyone, including yours truly, and people have to discover this by trial and error or by online resources.
Apple's official docs on this issue are also ambiguous though, as a user trying to download an owned app will encounter the message, "Are you sure you want to buy and download [app name]? Your account will be
debited for this purchase and your application will begin to download immediately."
Only after the user clicks "Buy" does a reassuring second message appear acknowledging a prior purchase - "You have already purchased this item. To download it again for free, select OK".
This second message should have been the first and only message upon attempting the redownload. After all, the user is logged in with that account if this stage of the process is reached, so this can easily be determined.
A clearer approach would be to remove the price from the text copy of the button ($0.99 BUY) since the user will not be charged that price when clicking that button, as well as to remove the "buy" text because most people will interpret that word to mean an exchange of money unless $0.00 is explicitly written alongside it.
But writing ($0.00 BUY) is also misleading because the retail price of that item is not free. So an improvement would be something like my proposal in figure 2 (second image above), with the text (REDOWNLOAD). It could even be ($0.00 REDOWNLOAD) or (FREE REDOWNLOAD) to make it absolutely clear.
Tapping the buy button again in Mobile iTunes on iOS devices, on the other hand, is much clearer, as it first prompts the second of the two earlier messages. It still suffers the issue of saying "buy" though.
The best implemented example is the "Update" button for a previously purchased app. Updates are free for owned apps, so it gets to avoid the buying concept altogether and throws the message, "This update is free because you own a previous version of this item. To get this update now, select OK".
These issues need to be fixed, and probably exist as a relic of the pre-app days of the iTunes Store, when users were not allowed to redownload music or other media. It's your move, iTunes team.