Ok, found it.
If you have Change with Buttons switch on in Settings > Sounds, the icon says Sound Effects instead of Volume. This might be intentional on Apple's part, to make sure you realize you are also changing the volume of the system sounds (including ringing and alterts) as well as the audio in your apps.
If the Change with Buttons switch is turned off, then the system sounds remain at the level shown in the Ringer and Alerts slider above the button, and the volume icon says "Volume". If it is on, the volume for system sounds is the same as for all other audio, and the volume icon says "Sound Effects"
I prefer to leave the button off, so I know that adjusting music or other audio won't keep me from hearing important alters. If I want the alerts silenced, I can still use Mute. That's what it's for.
Note: I'm guessing they chose Sound Effects because the ringer and alert sounds are not the only sound affected. Pretty much all the system sounds are affected: keyboard clicks, lock sound, etc.