Hi Michelle,
Editing is a deeper process than proofreading. Basically, proofreading is just intended to catch surface errors, while editing (as you said, too, there are several types within that terms) takes meaning, organization, clarity, accuracy, completeness, consistency, etc. into account. Depending on the level of editing, a client may want these things just marked/pointed out, or s/he may want fully written suggestions for how to do it better.
Here are a few helpful links. Some are in academic rather than business terms, but don't worry about that. They get to the same basic points.
http://www.unc.edu/depts/wcweb/handouts/proofread.html
http://deannahoak.com/2005/08/31/p188/
http://www.fonerbooks.com/editor.htm
http://writing.colostate.edu/guides/processes/editing/
Yes, proofing/editing can be a viable specialty option. I don't currently do anything but proofing, editing, and writing now, except for occasional reminder service or submission assistance for writing/editing clients.
I agree with the others that there's not really a degree or certification anyone cares about. Experience matters a lot more. Clients like to hear about you from others with whom you've worked and/or have a short-term trial project with you themselves before going for the big work. I think in this way, proofing/editing is like any other specialty: In a client's eyes, the real proof is in the pudding.
