What I Do

Substantive Editing
In a substantive edit, I look at plot, character development, pacing, story progression, effective chapter breaks, word usage, dialogue, etc. I take into consideration your goals as an author and your intended audience, and I help you make sure your story is the best it can be. I ask questions, make suggestions, and help you avoid pitfalls and problems that would weaken your story or alienate your audience.
I also look at broader issues of writing style--if you tend to overuse a particular phrase or descriptor, or if you make the same grammar/stylistic mistake often, I'll point it out and help you avoid it. Other nitty gritty grammar correction would wait until the copy edit.
This is typically the first edit I would do after you've completed writing. It might involve sending documents back and forth for a while until you're satisfied with your story.

Copy Editing
This edit would normally take place after substantive editing; the story is how you want it, and now we're looking at the tighter mechanics of things. In a copy edit, I clean up grammar, spelling, punctuation, word usage, and stylistic issues--all those little nit-picky rules that drive you crazy. At the end of the copy edit, you'll have a polished, professional piece, ready for the next step.