Copy edit is basically one step up from proofreading. Where the scope of the proofreader is generally limited to spotting typographical errors, misspellings and really gross errors in presentation, the copy editor adds grammar to the mix.
Copy editors generally follow a set of hard and fast rules about how to use punctuation and terminology, and they don't pay a lot of attention to the overall structure of your composition or even the meaning of a sentence.
It is when the editor is asked how to improve the manuscript. This is not cheating on the author's part, it's an honest admission that it's impossible to read your own work through somebody else's eyes
While a copy editor or a proofreader can do their work one sentence at a time, a hard editor should read the whole book through once before trying to edit it.
A technical edit is somewhat akin to "fact checking" and, depending on the manuscript, can end up being exactly the same thing. Some technical edits go far beyond simply reading a text with an expert eye and picking out flaws in logic or out-and-out mistakes.
Technical editors of computer books, for example, are required to verify computer code in the book and on any accompanying CD.
Technical editors must be experts in their field, not in English grammar.
Proofreading should be performed by a number of good readers, the more who fit your production schedule, the merrier.
The manuscript should be given to proofreaders in the final, typeset, form.
Aside from the possibility of errors being introduced by whomever does the typesetting, it's just easier for most people to pick out errors in a text that looks like a real book instead of double-spaced paper.
Proofreaders should really restrain themselves from commenting on iffy grammar and stick to mistakes.