On the iPhone the Visual Voicemail (voicemail screen) uses data. Basically all the voicemail messages are transferred to your phone using data.
Now if you call your voicemail (holding down the "1" let or by calling your own cell number) then that uses minutes.
Learn how connect your AT&T holiday gifts at Unwrapped on Wednesday, 12/27 (1-4pm ET)!
Is the iPhone X worth it? Find out why it totally is!
Find out how to track your iPhone's delivery!