Self publishing is the bastard stepchild of the book world. The only thing worse according to many is vanity press. Self publishing has a reputation that makes that term synonymous with a slush pile of unedited, poorly written dreck.
Now that publishing is changing, and self publishing is having a few successes, there are some self published authors who are trying to use the term "indie" to refer to themselves. The problem is that the term is already taken. If self pubbers want to use a different term to describe themselves, more power to them. But they shouldn't do it by preempting a term that has been in use in the publishing business for decades.
An indie author is someone signed with an indie press. An indie press is also sometimes known as a small press, but not always. An independent press is to publishing as an independent record label is to the music industry. It's not owned by a large conglomerate which is then owned by an even larger media company. It's a stand-alone business.
Wiki has several pertinent sentences as well:
The terms "small press", "indie publisher", and "independent press" are often used interchangeably, with "independent press" defined as publishers that are not part of large conglomerates or multinational corporation.
The majority of small presses are independent or indie publishers, this means that they are separate from the handful of major publishing house conglomerates, such as Random House or Hachette. The term 'indie publisher' should not be confused with 'self publisher', which is where the author publishes only their own books.
We don't consider an indie music artist as someone putting out records in his or her basement. We consider them musicians signed with an indie label instead of one of the big music companies like Sony or Warner. The same concept applies with indie authors and indie pubs.
Why does it matter? It matters because conflating indie with self publication confuses the reader. And confusing/deceiving the reader is a bad thing. I don't care how many extra sales you think you'll get, once deceived, a reader will not only NOT buy your book, they'll tell every other person they can not to buy your book.
Indies are true publishing houses. They are a PRESS. They publish more than the work of a single author. They have editors who acquire or reject based on taste and quality. This is an entirely different thing from self publication.
Most writers I know are aware that words have power. How you use them is important. Using a term that means something specific to many people in the industry and pretending it means something else is a choice. And I'm not going to have a very high opinion of those who engage in that practice.
Don't like the self-pub label? Fine. But don't steal a well known industry term and use it to mask what you're really doing.