Structural editors come in closer to the beginning of the job. They look at the whole piece. Whether it's an article, chapter or book. They look at things like "what genre is this?" And "does it flow logically from one section to another." And "Is the author using all five senses to describe people, places and things?"
Copy editors come in at the end of the job, when the draft is nearly ready to send to the publisher. They read every word, and examine at every bit of punctuation. A good copy editor is invaluable., and will save you from embarrassing typos, spelling errors, and convoluted sentences.
Structural editors are harder to find, and their hourly rates are higher than copy editors. It's a good idea to ask for references and samples of previous work. A good place to hire freelance editors is the Editorial Freelancers Association (EFA).