While editing and proofreading are offer used interchangeably, they are different processes. Editing refers to the content of the writing, while proofreading refers to the technicals such as grammar and spelling.
When your writing is edited, the expert offers ways to improve the language, including tone, clarity, structure, and flow of the writing. The editing process often takes multiple drafts to improve the writing. Editors will also check that the writing is appropriate to the task, asking what is the purpose of the writing and does it fit that purpose? There are four main types of writing and each of those types is appropriate for a different purpose: expository, descriptive, persuasive, and and narrative. A research paper or textbook will be expository, for example, white poetry and fiction is descriptive. Different types of writing have different purposes and will be edited with that purpose in mind. An editor of a textbook isn't going to look for plot holes or characterization problems, while an editor of a fiction novel isn't going to worry about citations or a clear thesis statement.
For example, I work on college application essays, which are mostly narrative with a persuasive subtext. Part of my editing process is to make sure the essay is answering the prompt. For a college application essay, it's appropriate to use first person, while this is not appropriate for, say, a research paper. I look to see if the essay grabs the attention of the reader and makes the reader want to continue reading. Does the essay give the reader a sense of who the applicant is and why the applicant would be an asset to the college or university? Does the essay and applicant stand out against the hundreds or thousands of other applicants? These questions must be answered in a college application essay and will part of my editing.
The next step in the process is copy-editing. Once the content is finished editing, the copy editor fine-tunes the writing to make it presentable. The copy editor will check for passive voice, awkward dialogue, vague usages of words like "it," or unnecessary repetition. Sometimes this step is included in the editing process, depending on the editor. Copy editing are often called "line editors" as they fine tune writing line by line. The copy editor will also take care of any glaring grammatical mistakes or other technical problem as they go.
The final step is the nitty gritty: proofreading. This is the final check for grammar, punctuation, spelling, or anything else the editor or copy editor missed. Proofreading is the safety net to perfect the writing so it is ready for publication. This step is often a single draft.
All the steps are important and necessary, and you should be clear with your editor as to what you are wanting. Do you want feedback on content and story or are you just wanting a second pair of eyes on the punctuation? Also, the editor should make it clear on whether they will be editing, copy editing, or proofreading. Some editors will provide all three, but this should be clarified before hiring the editor. This is the way I work: I'll start with content, often for several drafts, and when the writing is in good shape, I'll go through a final look at technicals. I will also reread a "final draft" to make sure it is, in fact, a final draft.