So, I've read a couple of things about different types of editing, and not shockingly, people don't quite have the lingo down. That's in part because the lingo does not, in fact, make sense--so don't feel bad if it confuses you!
So, what is the difference between the different forms of editing? Well, that's a fun question, because when I was an editor, my job varied greatly. Sometimes I edited something by tightening it up a bit. Sometimes I edited something by throwing it into the garbage and starting again from scratch.
The job of an editor is basically to ensure that the prose that appears in a publication or from a publisher is up to snuff, however that business may define "snuff." If your publication has a particular voice, you make sure that the article is written in that voice. If your publication has 20 available inches of column space, you make sure that the article will take up no more and no less than 20 inches of column space. If your publishing house expects all books in a series to follow a certain format, you make sure that book follows that format.
There is, as this person discovered, an enormous difference between an editor and a copy editor. As I mentioned, when I worked in book publishing as an editor, I was never ever a copy editor. This in no way impaired my career as an editor, any more than never having worked as a cover artist would have--they are two very different skill sets, and being good at one does not mean you'll be any good at the other.
Copy editors provide what you think of when you think of proofreading. They call it copy editing, but it is not editing. They are not editing copy, they are proofreading copy.
But why don't they call it proofreading? you shriek. Well, back in the days of yore, manuscripts had to be set into type in order to be printed. Typesetters were not college-educated fancy people like editors and copy editors. They wore overalls, never went to school, spat, drank a lot, and tended to physically assault people who criticized their work. They were infamous for being to all appearances completely illiterate and possibly subhuman.
The copy editor would polish the manuscript to perfection. Then the typesetters would take this manuscript and produce a proof, which was invariably a HUGE mess, not even recognizable as a written language. So you had a copy editor give the proof what was called a proofread, to fix what the horrible typesetters had done. If a copy editor read only proofs, they were called a proofreader.
The further you get in the production process, the less stuff you can change (especially if something is being set in type, as in the days of yore). So proofreaders couldn't change much--a proofreader couldn't really say, "This sentence is awkward. You should rewrite it," because it was just too late for that. Copy editors could, because they were working with the manuscript earlier in the process. So when people act like copy editing and proofreading are very different, that's why. Proofreading jobs also typically were entry-level jobs--a person would start as a proofreader and get promoted up to copy editor. But proofreaders and copy editors use the same skill set.
Nowadays we just convert files, and stuff usually doesn't get all messed up in the process. So the difference between a copy edit and a proofread has gotten more academic. Within the industry, people still distinguish, because stuff can still go very wrong after something's been laid out. But you can call it a "copy edit/proofread," which if memory serves is what I told my first copy editor, and he was not confused at all (unlike my second).
Now line editing is actually editing, done by editors. When you line edit you fix all the clunky crap. Maybe you catch some typos, too, but the copy editors are better at that sort of thing than you are--your primary focus is on making something read well. You also are altering the voice of the piece so that it matches the voice of your publication. When I had stuff I didn't have to throw away and rewrite (which is called ghostwriting, and I did a lot of that), I was line editing.
Story editing is also editing. It's just taking a broader view. If you give me something to read, and I say, You need to cut a ton of exposition, it takes too long to get to the plot, and the ending is unsatisfying, then that is a story edit. (Sometime we called this a structural edit.)
Generally when I'm in a writers' group or am beta reading for someone, I'm doing a story edit. Unless something is awkward or doesn't make sense, I don't feel like it's appropriate for me to line edit--it's overstepping. People should write their own stuff, and I certainly don't want every story out there to read like it was written by me--that would suck!
Sometimes people really want line editing, because they're insecure about their writing. My feeling is that you need to ask yourself if you're comfortable having someone else basically rewrite your book. If you're just nervous about the quality of your writing, I think that if you take your work to a critique group or two and no one complains, then you can calm down. If they do complain, you can revise and see where it gets you. A decent copy editor or beta reader will mark anything super awkward or flat-out incomprehensible, and the rest you can judge according to your own taste.
There are some other kinds of editors--and some, although not all, of them actually edit. I've never been one of these:
Developmental editor. You can see my bafflement at this kind of editing if you scroll down to the comments here, but then someone else explained that another term for "developmental editor" is "writing teacher." Made ever so much more sense.
Technical editor. NOT a copy editor! Or even a proofreader! Technical editors are actual editors who specialize in technical writing, like user's manuals.
Managing editor. A managing editor does not edit (although they'll look stuff over). A managing editor makes sure things happen when they are supposed to and will mercilessly beat those hapless employees who fall behind. Think dominatrix, only less well-paid.
Acquisitions editor. The person who accepts or rejects books for publishers (if sales and marketing will let them). Doesn't edit but will request changes to a book to make it acceptable.
