According to Editors Canada, there are four basic types, or stages, of editing:
Substantive or Structural Editing: Clarifying and reorganizing content and structure
Stylistic Editing: Making meaning clear, fine-tuning language, eliminating slang and jargon
Copy Editing: Fixing errors in grammar, spelling, punctuation, etc., checking for consistency
Proofreading: Making sure edited material is in proper design format, final check for mistakes before the material goes to print / goes live
Some projects are created by grammar gurus and only need some fine-tuning (stylistic editing). Other projects are created by genius intellectuals but still need grammar and punctuation fixes (copy editing). Others need the whole shebang. The type of editing required depends on what kind of project/text/material you have and where you're at in the process.
Hopefully that helps a bit to clarify the different types of editing. My clients primarily ask for copy editing and stylistic editing. I offer all four types.