There is a difference between copyediting and proofreading in terms of what each service entails and the depth of editing involved.
Copyediting is a light edit that looks for errors in grammar, punctuation, spelling, syntax, and word usage. A copy editor will also check for consistency in style and formatting, and will make sure the text flows well and is easy to read.
Proofreading is a more in-depth edit that looks for all of the above errors, as well as typos and inaccuracies in the text. A proofreader will also check that all the text, headings, page numbers, and other elements are in the correct order and correspond with each other.
In general, copyediting is done before proofreading, as it is easier to spot and fix errors when the text is free of typos and other inconsistencies.