When I open the "ringtone store" directly from inside the iPhone settings for ringtones, there is a special section available for alert tones, rather than ringtones (which will end up in the "alert tone" list in iOS if you purchase them, rather than in the ringtone list where ringtones will end up).
But there are only around 50 such alert sounds listed there (and most are soundbits from contemporary movies and similar, rather than your classical alert and notification sounds), and I cannot for the life of me find any way to expand this list? To make things even worse, when using the search feature in this store, the results never contain any alert tones at all, only ringtones?!
For a company that has seemingly locked down any possibility for users to add their own custom alert tones (or haven't they?), this seems even more crazy, so I'd be super happy if someone would tell me that I'm just blind and/or stupid, and that there is after all an easy way to both browse and search for lots of more alert tones in Apple's "tone store"?