There are many different approaches to the task of editing but these are the main ones.
Proofreading is the final check before publication. It looks at spelling, punctuation spacing and so on.
Copy-editing is a light or medium edit. It aims to achieve accuracy, clarity and consistency in a document. Copy-editing looks at correcting grammar, spelling, punctuation, and style (which includes capitalization, syntax and referencing).
Substantive editing (or content editing) examines the language, content, style and sentence structure of the document. It is not a rewrite but looks at the bigger picture in the way content is organised.
A substantive edit aims to improve presentation of the document, keeping the readership in mind. It includes rewording to improve the clarity and flow of the story. It examines tone, voice and syntax.
For our purposes at LifeStory Writing, a substantive edit includes copy-editing. For example, it will include a close check on punctuation, grammar, capitalization, quoting, syntax and referencing. We also provide detailed suggestions and ideas for redrafting.
For more information on editing (see here).
Other editing terms you may come across (particularly in larger publishing houses) include: line editing, stylistic, heavy, structural, developmental editing and indexing.