I know others have answered just as well as I can, but this question buzzed around in my head half the night so I'm gonna chime in anyway.
I think the easiest way to understand the difference between style and voice is via a comparison to music. Style is comprised of the chord progressions, themes, vocal production techniques, instruments of choice, etc. of each different type of music. You can listen to a song you've never heard before and know immediately what style it is (jazz, rock, classical, showtunes, rap, TV jingles, yodeling, etc).
In writing, style is similarly associated with different genres. A newspaper article does not sound like a fairy tale does not sound like a romance novel does not sound like Shakespeare.
Voice in music is often a literal voice. The Beatles and Nirvana are both rock groups, but it'd be hard to confuse the two. You'd never mistake Dolly Parton for Johnny Cash or vice-versa, even if they are both country singers. Voice is what makes you, you.
You know the neatest part of that? It just happens. You don't have to consciously create a voice. You "discover" your writing voice over time, just as a child may sing for years, but has to wait until maturity to find out whether she'll end up a soprano or alto (tenor or bass for the boys), whether you'll have the smooth sound of Frank Sinatra or the gravelly earthiness of Louis Armstrong.
Do you write long, flowery descriptions or short blunt phrases? Do you tend to write lots of dialogue or are you heavy on the action sequences? Do you write with a thesaurus by your side or stick to a simpler vocabulary? The answer to these and countless other similar questions comprise your voice. Your voice, in turn, will lend itself to styles/genres that best showcase those characteristics. As a singer, I have a very high light voice. I'd make a dandy Disney princess. Conversly, I've come to accept that I'll never be able to "rock," no matter how much I wish I could.