The term "editing" covers a lot of territory. There's copy editing, which is only looking for misspellings, typos, grammatical errors, and other problems with the mechanics of writing (also includes fact-checking).
Developmental editing taking a bigger picture view--developing the story and structure of the work.
There is also sort of general editing, which is more detailed than developmental, but less limited than copy editing (although it will likely include copy editing). This level of editing would include more style issues, point out logic problems, etc.
Technically, proofreading is none of this. Once a book has been through the editing and copyediting processes, it's sent off to a typesetter or compositor. They produce page proofs--a set of pages that shows how the book will appear in its final form. The proofreader compares these *proofs* to the file that was sent to the typesetter, to catch any errors that might have been introduced. In real proofreading, there are two sets of pages--one from the typesetter, and one from the publisher (with all the errors found by the copy editor fixed--this set should be as close to perfect as possible)--side by side. The proofreader looks for things like words hyphenated incorrectly at the end of a line, widows & orphans, broken type (less of an issue now that most proofs are digitally produced), layout problems, running heads, etc.
Most people equate proofreading with copy editing, but this is incorrect. Especially within the publishing industry.
Pricing depends greatly on what kind of editing you're talking about, how much experience the editor has, and what kind of material is being edited. Heavy duty editing will be more expensive than copy editing.