The difference between the singing and the voice, Tom Waits does it for me, first up his softer side, which is both more tuneful and less heartfelt (more storytelling than truth telling, though the two are entwined):

Tom Waits Martha (4:40)

I used to listen to this on a walkman way back when, walking home through the empty town late at night, Closing Time on one side of the cassette, The Times They Are a-Changin' on the other, both pretty much one instrument one voice--one all lovelorn the other protest music--great lyrics in both cases

Then there's Tom after he met Kathleen Brennan, worked up a showman role and bent his music into crazy shapes, but (for me) used the strange shapes to--over time--pick at the truth ever closer:

Tom Waits -- God's Away on Business (3:04)

From talking to people it seems his is a voice you either love or hate.  I love it.

Don't fight forces, use them R. Buckminster Fuller.