Proofreading is simply finding and fixing errors in spelling and grammar. It does not include formatting. It is superseded by editing concerns; good editing recognizes the right of the author to use unorthodox spelling or grammar if there’s a reason for it.
Editing is the art of adjusting the words so they say the best version of what the author meant. It does not mean applying someone else’s writing style.
Formatting includes textual formatting like italics and bold. It also includes creating the page layout. This covers headers and footers, page numbers, title pages and other front matter, and possibly the index and table of contents.
Design generally refers to the cover, though it may include illustrations for the interior.
Printing requires the creation of print-ready files and delivery to a printer. Independent publishing often uses online print-on-demand services.