Copy editing and proofreading as skills, have their origin in publishing houses. The proofreader would basically have two sheets of paper and if they were right handed they would compare the double-spaced copy (left side on their desk) with the single-spaced proof (right side on their desk) to ensure that amendments made on the copy had been transferred smoothly and that no new errors were introduced by the publishing team’s process – a process that included, among others, a copy editor, typesetter, and author.
These practices were from days and times when typewriters were used, and a typesetter would rekey the entire manuscript with the copy editor’s and author’s amendments, but these days most people do their writing on PCs, other computers, or using online applications and there is therefore less need for a typesetter to rekey the entire material.
In practice a proofreader would look left and right a lot, as you could imagine. When a proofreader was asked to look at a single sheet it was called a ‘blind proofread’, which meant there was no copy. Most proofreading nowadays is a blind proofread!
Traditional book publishers wouldn’t have a single ‘go to’ person to sort out the manuscript, as we sometimes have nowadays when hiring freelances, and although over time publishers have hired out freelances to cut costs, they would still follow a rigorous quality control process. They’d do it in stages to prepare the manuscript for publishing and to help catch errors before it was too late.