The visual voicemail personal greeting on iPhone may not match the standard voicemail personal greeting.
This is most likely caused by dialing into your voicemail, instead of using visual voicemail, to change an option such as new greeting, or changing to or from the default greeting.
The recommended way to change your voicemail greeting is by choosing Phone > Voicemail > Greeting, which will then in turn synchronize with your standard voicemail greeting so they both are the same.
In most cases, voicemail greeting changes made by dialing your voicemail will be synced back to visual voicemail on iPhone if you are using iPhone Software 1.1.3 or later.