What`s the difference between rel="publisher" and rel="author"

Selected answers from the Dumb SEO Questions Facebook & G+ community.

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  Mimetix: Hi guys, when linking your website to google+, i am a bit confused about the difference between rel="publisher" and rel="author"
  Should i use for publisher my google plus page, and in author use my google plus profile? If i do so, google structured data testing tool only finds my profile. If i just set g+ page on both, it finds my page. What do you recommend me?
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  David Kutcher: Company or Institution is the publisher and Page, author is always a person and Profile.
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  Mimetix: +David Kutcher ;yes but, can i use both? use g+ page of my company for publisher  ;and g+ personal profile for authorship?
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  David Kutcher: You could, but it's not proper. Plus the rich snippet bio photo shown in Google SERP is almost exclusively reserved for people (recognized photos) so you'd lose that benefit... As well as others.
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  Adam Heaton: Why not both +David Kutcher? Surely it makes sense to have the company page set up as the publisher and the main person of contact for the company set up as the author? Makes sense to me anyway.
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  David Kutcher: Yes +Adam Heaton Company/Page/Publisher and Person/Profile/Author.
  
  My apologies, got confused as I was talking to a company.
  
  Profiles need to always be People. Authors need to always be People.
  
  Publishers can be People/Profiles or Pages, but I recommend Pages.
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  Adam Heaton: Apologies +David Kutcher, I must have misunderstood you.
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  Emmett Smith: +Mimetix you can use both if it is implemented right.
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  Mimetix: +Emmett Smith can you send me a link with more info? What do you mean with "correctly"? My website is mimetix(dot)com if helps