A brief overview of each craft is provided, below. Additionally, the UK-based Society for Editors and Proofreaders provides a factsheet on copyediting vs. proofreading that you may find useful. Often the terms copyediting and proofreading are used interchangeably, but the tasks involved in each differ substantially.
Editing text for grammar, syntax, word choice and usage, spelling, punctuation, and other style issues; consistency in style (e.g., spelling, capitalisation, date and number formats) and language, and internal consistency of facts; flow (i.e., clear and logical connections between phrases, clauses, sentences, paragraphs, and sections), tone (with consideration to audience), clarity of meaning, and ease of reading; removing ambiguity, wordiness, and needless repetition; appropriate use of technical and specialised terminology, including discipline-specific terms (reducing jargon, if possible), abbreviations, and units of measurement; formatting references and citations to appropriate style; consistency in presentation of tables, figures (inc. diagrams and illustrations), and lists; checking for broken links; and flagging potential legal issues.
Copyediting does not include substantive or structural editing, fact-checking, or the checking of complex mathematical calculations.
Applying genre-appropriate document, page, and element layout to manuscripts so that appearance is consistent throughout, including: the application of title, heading, paragraph, header and footer styles; font type, colour, size, alignment, and kerning; standardising margins, paragraph and line spacing; adding section and page breaks, and controlling “widows” and “orphans;” creating a table of contents, list of figures, and list of tables; standardising the presentation of tables, lists, and captions; reformatting tables, including re-orienting pages to landscape and moving page numbers; adding bookmarks and cross-references; changing page number styles (Roman/Arabic); preparing PDF and/or PDF/A document versions with fonts embedded and clickable links.
Speaking plainly, document formatting can transform a "sow's ear" into a "silk purse" (despite the idiom saying otherwise)!