If something is existing, it's real. When you make a list of existing mammals, you can't include unicorns, because they don't really exist.
Something that's real can be said to exist, or to be existing. The existing laws in your state are the ones that are actually on the books, and your existing friends are the ones you really have, and who are all alive and well. The verb exist, at the root of the adjective existing, comes from the Latin existere, "come into being," from a combination of ex, "out," and sistere, "take a stand."