It's a question that I get asked often by first-time authors so my answer is aimed at those who have no previous knowledge or experience of the publishing industry.
Copy-editing and proofreading complement one another but they are two distinct functions with their own disciplines and their own place in the process. These are two stages of the editorial process which work together on your final draft to ensure that your publication is the best that it can be when it goes to market. They are often preceded by the beta reading and developmental/substantive editing stages.
Let's use an analogy to explain what they are and how they fit together.
Copy-editing is the horse. It comes first. Generally, copy-editing is carried out using Word where time-saving editing tools can be used and Track Changes is employed for the mark-up.
In the words of the SfEP:
"Copy-editing takes the raw material (the 'copy': anything from a novel to a web page) and makes it ready for publication as a book, article, website, broadcast, menu, flyer, game or even a tee-shirt.
The aim of copy-editing is to ensure that whatever appears in public is accurate, easy to follow, fit for purpose and free of error, omission, inconsistency and repetition. This process picks up embarrassing mistakes, ambiguities and anomalies, alerts the client to possible legal problems and analyses the document structure for the typesetter/designer."
Copy-editing is a big investment in time. It is a complicated beast covering everything from plot/character consistency to grammar and typos and will lead to, sometimes quite substantial, revisions by the author. There will always be something to clear up afterwards. Which brings us on to the next stage.
Proofreading is the cart. It comes last. Without the horse, the cart is cumbersome to move forward. A proofreader will work on the document in its final format whether that is a Word, PDF, epub or mobi file.
Again, the SfEP puts it succinctly:
"After material has been copy-edited, the publisher sends it to a designer or typesetter. Their work is then displayed or printed, and that is the proof – proof that it is ready for publication. Proofreading is the quality check and tidy-up ... A proofreader looks for consistency in usage and presentation, and accuracy in text, images and layout, but cannot be responsible for the author's or copy-editor's work."
Proofreading is just as vital for transporting your book to market but it is less complex and more focused on the mechanics. Providing the horse has been put in harness, the cart will move along quickly and smoothly.
I'm sure that you can guess where this analogy is leading. That's right. You can't put the cart before the horse. First your manuscript is copy-edited then, when all of your changes are made and it's in its final format, you get it proofread. Asking for a proofread of a document that has not been copy-edited will either lead to refusal or a longer, more expensive process than you were expecting. A proofreader's rates are set on their expectation that they are providing the final quality check and tidy-up. If the manuscript you send them is still at a stage that requires something more in depth, there will be adverse consequences to your deadline and/or your budget.
In the best case scenario you would hire two different professionals. One to copy-edit your document and the other to proofread it once the alterations suggested by the copy-editor have been made and the copy is in its final format. The use of separate individuals gives you two different pairs of expert eyes which will give your text the best chance of being as close to 'perfect' as possible when it goes public. If, however, you do not have the time or the budget for a separate copy-edit and proofread then you have the option of commissioning a proof edit. You will lose the advantage gained from the second pair of eyes but your publication will still be significantly better in terms of quality and clarity than if it had missed the editorial horse and cart completely.