When you silence the ringer the alarm does still sound.
When you turn the phone off it won't sound for anything, calls or alarms.
Not sure if you are aware, but the iPhone's sleep is different to any other phone I've had. If you press the sleep button the screen turns off and the keypad locks. Alarms still sound and calls can be received. If you want to check the phone's status (missed calls, texts, the time) you press any button and the screen lights up showing you this and asking if you would like to unlock.
Hope this helps