What is a Freelance?
First, is it freelance or freelancer? Well, either! But freelance may be a verb, adjective, noun or adverb. Freelancer is only a noun, poor thing!
So whether you are a copy-editor or proofreader you may call yourself a freelance or a freelancer.
Word Origin
Well, if you are setting out to be a freelance copy-editor or proofreader you have a noble ancestry. In medieval times fighting men were hired. Some would have owed allegiance to a lord, but others were free to sell their services: they were free lances. The pen may be mightier than the sword or the lance and swords may be beaten into ploughshares but we should not forget our ancestry!