To date, I have always had whatever carrier's vvm app as the only option. This ZTE Zmax Pro has almost a 100% Google stock Android OS, no overlay, no skin, all Google apps...stock email is Gmail, dialer is Google phone, even the messenger is Google. The dialer has VVM, but the T-Mobile app is on there too. Wasn't this baked into stock Android M? So, can't I just disable T-Mobile's VVM app?
Also, what's the difference between T-Mobile's Caller ID powered by Hiya, and the Hiya app on the Play Store that's free?
As far as the Caller ID issue others spoke of, I found that the Contacts app did not have "contacts" permissions set correctly. Anyone already in my contacts was showing numbers, but no names. This seems to be resolved. I just got this phone for backup, so there may have been an update already that fixed this.
I believe I can add one difference, outside the UI, and that is that VMs deleted from the stock app are not actually deleted from the account. All the voicemails on the phone which were deleted stayed in my inbox when checking the T-Mo app or dialing into the VM inbox. So, seems the stock app deletes messages from phone but the T-Mo app deletes from inbox at T-Mobile.
Manage your T-Mobile account