You see a lot written about the types of editing--copyediting, line editing, developmental editing, etc.--but not much about different kinds of editor. In my experience, the editor's background is more indicative of what you'll get than the "editing function" they claim to perform. Bear in mind that I'm offering my four kinds of editor as food for thought--they're just generalizations from my experience:
1. Amateur editors are avid readers with an interest in fixing all the mistakes they see (or think they see) in the books they read. They're probably fine with proofreading for typos, but they rarely know much of anything about grammar, usage, or style beyond what they've picked up from Google searches. KB seems to have a surplus of these editors, probably because they come cheap.
2. The-best-writer-in-the-room-at-the-time editors happened to be there at start-up and got assigned the task of editing and hiring editors. You'd be surprised how many firms, institutions, and even presses employ such people. It's one of the reasons that "editor at such-and-such press" means nothing to me; they're often no better than amateurs.
3. Trained copy editors have a technical writing or copyediting diploma. They're usually much more knowledgeable than the first two about the conventions you find in the Chicago Manual of Style and the handbooks. But the only style they seem to know is the stripped-down plain style familiar to any reader of newspapers, magazines, and the big writers in the popular genres. Their weakness, in my experience, is over-editing. When someone complains about an editor sucking the life out of something--assuming there was life there to suck out--or complains that all the characters sound the same, they probably had a copyeditor. Making everything align with the generic pattern, after all, is what they're trained to do.
4. I call the fourth group MFA editors, not because very many have MFAs, but because they all come from an academic background in the humanities. Where copyeditors focus on conventions, MFA editors focus on style. They'll be weaker on handbook conventions, but they'll have a better understanding of your voice and what you're trying to achieve. Of course, you have to know what you're trying to achieve to get the most from an MFA editor.
My 2 cents.