In English Language editing, the editor merely fixes grammar, spelling and by extension punctuation and capitalization errors, to present better English.
Proofreading used to be a check that the handwritten manuscript had been correctly typed. Today proofreading will check that the fonts are correctly used, and that the pages are numbered. The proofreading would also check that figures and tables are correctly referred to in the text, and that all figures are clear and legible.
Copy editing polishes the text to make it more readable. For example, two adjacent headings at different levels, with no introductory text could have obvious introducing text written and inserted. Furthermore, copy editing would e.g., look for and try to fix any errors in the citations. Page breaks could be improved.
None of the above activities is allowed to add any intellectual input. Any ambiguities must be referred back to the author for resolution.
See https://en.wikipedia.org/wiki/Copy_editing for more detail
1. Overall Editing involves making changes to improve structure, readability, and language use.
2. Language Editing involves editing to improve language use. Particularly, it involves editing text written by non-native speakers to read more like native speakers would write.
3. Proofreading is a basic edit for grammar, spelling, proper word choice, formatting, etc, without regard to readability.
4. Copy Editing is what the journal does after your final submission, to get the manuscript ready for publication.
The answer will probably differ from service to service; my broad definitions would be as follows:
1. Language editing: focuses on the clarity, readability, and accurateness of the grammar and expression. This service is frequently used by ESL (English as a Second Language) authors to ensure their expression sounds fluent. It will almost certainly be incorporated into both editing and proofreading services for authors who need it. Make sure you let your editor know beforehand if you need this service.
2. Proofreading corrects grammar and expression, formatting, referencing and citation. It does not usually focus on content at all. It is often a second-pass service, used after a round of copy-editing has occurred.
3. Copy editing incorporates proofreading + commentary and advice on content. A good copy-editor will comment on whether your thesis is clear, your sections are in the most effective order, your evidence is strong enough, your logic is faulty, your unique research question is clearly articulated, and so on.
No reputable cop-editor/proofreader will re-write or write material for you; avoid editor's who offer this service as it is deeply unethical and could land you in trouble.
I am a published academic author and journal editor who also offers an academic editing service. If you would like more advice or are interested in my services, you can find me at www.readwriteperfect.com. Good luck with your publication!