edit:  "To prepare, set in order for publication" OED

proofread: "To read (text, esp. in proof) in order to find and mark errors for correction." OED

Proofreading

After you’ve drafted your paper, sought feedback, and revised, you might be ready to begin editing or proofreading your work. It can be difficult to find your own mistakes within your papers, so here are some resources to support you along the way! - Taken from Proofreading Strategies

To Learn More About Proofreading

1. Proofreading Strategies
2. Organization Within Paragraphs
3. Writing Center Handouts on Clarity: Grammar & Punctuation

Editing

One of the last big steps involved in any project is that of editing—when you look for changes that can be made which won't change the core/bulk of your project. At the Knowledge Market, making edits means making those small changes that improve readability, clarity, elegance, and respect. 

We recommend that the types of edits that can happen during this phase be saved for the last bit of your time with this project—if you're looking to make big changes, think about looking into "revisions."

How Does Editing Work?

Changes that can be made during the editing step include:

• Sentence-level changes
• Word changes
• Spelling changes
• Paragraph organization
• Title changes
• Deleting unhelpful content
• Adding material to help your reader

To Learn More About Editing

1. Active and Passive Voice
2. Apostrophes *
3. Bias-free Language
4. Capitalization
5. Commas *
6. Confused Words
7. Dashes
8. Pronoun Use - You Attitude
9. Proofreading Strategies
10. Reverse Outline
11. Run-on Sentences
12. Sentence Fragments
13. The Colon
14. The Semi-colon *
15. Types of Sentences
16. Wordiness