Hemingway on Safari
I don't think writers have voice. Narrators have voice, and often writers are the narrators of their fiction, which lends to the idea that writers have a voice--which they're frequently encouraged to go find, somehow.
I think they would do better striving to understand narrative voice and how it influences a story. I'm certainly no expert--that's why I'm writing this blog--but here are my thoughts.
Why make the distinction between writer's voice and narrator voice? Because the same narrative voice won't work with each story. Some stories might yearn for a detached third-person observer narrator, others might benefit from a third-person commentator narration. Neither is deep in the character's head--a function of narrative distance. One offers only raw detail and facts. The other accompanies story with opinion, either through tone or more directly. (And there are other types of narrators, such as the unreliable narrator. These are just a couple examples.)
Voice changes with narrative distance, which is how close the narrator is to the mind of the point-of-view (POV) character. Some authors call it psychic distance.
A distant narrator--still limited to the POV of a single character for this example, remains outside of the character's head. John stepped onto the porch. It was early summer. It was hot. He was sweating.
Closer narrative distance--the writer reveals some internal mood or thought. John hated the heat. He hated sweating. He wasn't too fond of the porch, either.
Then, at its closest--the narrative becomes a kind of stream-of-conscious writing. Damn heat. Damn bugs. Porch needs fixin'. The voice is no longer a non-person narrator. It is the character's voice.
Now, along with this, there are omniscient POVs, which can be detached or also can comment on the story. There is also first-person, which tends to be deep, but not always. First person can, if the author chooses, be surprisingly distant.
All of this comes down to author choice. What kind of tense, narrator, distance and perspective used all define the storytelling technique, which in turn contributes to tone and mood of the story. They're important tools that deserve some thought in nearly any story.
In the end, each writer will also have some level of their own voice they can't escape. A familiar fan might recognize the style and voice of an author that uses a different name. (Personally, I think a good writer would be hard to recognize due to a strong narrative voice.)
Note that narrative distance is different than aesthetic distance.
Writer of speculative fiction. Current work in progress is an untitled dark fantasy novella.