I think you are, AND a home moorer. An analogy might be if one parks their car in a public street, then gets into a truck. You are still a "car owner" because you were the last one to have driven your car, so any penalties relating to excess parking, obstruction, no insurance or road tax etc will still apply. At the same time, you're also a truck driver because you are now in a truck, driving it.
CCer is a fairly neutral, commonplace term for "a boat(er) without a home mooring or other place..........blahblahblah" and is much easier to use in conversation. I don't think anything more than the distinction of the (no) home mooring arrangement, is applied by using the term.