Between fan fiction and published work and I'm not happy with those labels either. I thought about 'fan work and professional work' I thought about 'fan fiction and original fiction' and I thought about 'hard cover' and 'online'. It's hard for me to conceptualize the difference between the two. Not even 'one's published and the other's not' works any longer.
When I was a teenager I read a lot of fanfiction. First fan sites and then I found Fanfiction.net. It was an extension of the books I read. The difference used to be that the former were amateurs published online and the latter was the work of a professional I could hold in my hand. As I read more I realized the truth of SturgeonsLaw: '90 percent of what I found in fanfiction was crud'. I reasoned this was because (like me at the time) these authors were immature teenagers with immature skills. The books I read were written by adult writers whose age has matured their skills. That's why I paid money for the latter and critique to the former.
Then I grew older and my skills matured. The people on my author alert list on fanfiction.net grew older and their skills matured. It got to the point where the stuff I read online (still fanfiction) was as good or better than the stuff on my bookshelf (some of it anyway). Around the same time I learned that some people were self-publishing. I learned more about the process and it sounded as easy as publishing at an online archive of original fiction, i.e. fictionpress.com. This is where the line blurs.
If publishing on a marketplace site like Amazon is as easy and cheap as publishing on a free archive like Fictionpress than what's to stop an arrogant and immature wannabe writer (i.e. ME at age 15) from publishing what they think is a brilliant work of literary art and fully expecting others to pay to read it?
Nothing except their own talent. On the one hand this is great; the only obstacle to (let's be realistic) modest success is the author's determination to refine their skill and get their name out there. No more querying agents and working deals with publishers and waiting perhaps months for both of them to contact you only to get a standard rejection. Anyone with the drive can shoot for the stars!
On the other hand...."heroes that are not yet ready for their journey are forced to turn back until they have matured sufficiently to handle the task." That's a quote from TvTropes' article on Threshold Guardians and I couldn't have put it better myself. The guardian in this case could be the agent or publisher. Unlike the author, who could be their own best critic, they are emotionally detached from the book and can make an objective decision. A rejection might sting but the writer and their book will be better for it.
I am living proof of this. The sequel to "A Mage's Power" was reviewed by my Mom and she tried really hard not to hurt my feelings. Even so I felt shaken and lost. I thought the manuscript was great; I planned its story arc, I revised each chapter as I wrote it and then revised the whole book twice over. I thought it was fantastic. My mom didn't think so. I returned to the manuscript to find the problem and when I did it hit me over the head.
Scenes were rushed. Wording was poor. World Building that I thought was crystal clear (because I spent weeks working it out) was not adequately explained. I ended up increasing the length by 1/3 to better develop the plot and basic events etc. Then I thanked my mom for pointing out the many problems. I would have been mortified if I put that on the Internet for anyone to see.
Of course, now that I've revised it three or more times I'm thrilled that I can use Amazon or Smashwords or whatever to get my book into the hands of fantasy readers everywhere. I'm merely glad someone advised me against launching too soon. THAT, I believe, is the difference between the two groups. It's not about published status or the material its made of. It's time and effort and patience that separate the successful authors from the rest.