A copyedit comes after you've completed your developmental edits, when you're largely satisfied with all the global aspects of your story. Copyediitng focuses on the mechanics of your manuscript, including punctuation, syntax, diction, and checking for factual inconsistencies. This is the stage where you'll want to cut commas and words, correct and unify regional spelling, and ensure consistency with any style guide you're using.
The line edit, on the other hand, focuses on the overall style and consistency of your narrative. Line edits help shake out redundancies in your text, clean up your dialogue, flag tonal shifts and unnatural phrasing, and suggest changes that can clarify or enhance your meaning.
As a freelancer, I commonly unify the copyedit and the line edit and deliver them at the same time, allowing for fewer editorial and revision passes.