I'm guessing that an independent / small label will do different things then a large label. But I have always been under the impression that a music label is supposed to be taking care of most aspects of your business. From getting you studio time, to finding a producer, helping to book venues, PR, marketing, getting your music distributed. There are also lots of partnerships in the music business, you'll see some artists who might be involved with a couple different companies. I'm guessing some of the bands who have a lot of success with indie labels go to a large label or large publishing company just for their distribution channels.
Like the EDM artist Deadmau5 used his own label Mau5trap for US/Canada but hooked up with Virgin for global distribution http://en.wikipedia.org/wiki/4x4%3D12 - I'm guessing that is also who ended up getting his album in Target. So it's a complicated landscape and I imagine what all a label does for an artist is fine tuned in the contract. Things like who actually owns the songs. More established artists may be able to keep actual ownership, whereas a new artist signed to a label may relinquish all rights to the work to the Publisher. I think L.A Reid owned Gaga's stuff but released her and her work from his label Island Def Jam prior to her blowing up into a superstar.
Yes, labels are typically the publishing company.
In the Deadmau5 example I his label would be the publishing company, own all the rights etc, and they used Virgin specifically for distribution.