So what is copy editing?
A copy editor makes sure that the text is correct in terms of spelling, grammar and sense; that there is consistency in terms of the story or message, and that facts are checked and true.
A copy editor's job involves either adhering to, or creating, a style guide - ensuring consistency in things like the way numbers are written, which words will be hyphenated, and decisions where there are alternative spellings.
In addition, a copy editor will shorten long sentences and/or paragraphs, check that the tone of voice is appropriate for the audience, and make sure there's nothing missing. For a more detailed explanation, visit the SfEP website.
The proofreader's job comes right at the end. When the copy editor has done their job and the author, publisher or client has approved it, it will go to print and a final proof will be made (or if it's web copy, an offline version or pdf will be created). Only at this very last point should it be proofread.
It's the proofreader's job to act as a quality check, not to check for consistency and accuracy - that should already have been done. It is often only at this last stage that illustrations, graphs and other elements are put together with the copy, and the proofreader must check these and their labels for consistency, accuracy and layout.
Page numbering is also often only put in at this stage and is something else that is the responsibility of the proofreader to check. For a very useful and more detailed explanation, visit the SfEP website.