No one can copyright your work. Copyright is present and automatic the moment you write anything. All pubishers do is register the work, which is really nothing more than placing a time stamp on it.
Short stories pubished in magazines are registered, as well, sometimes individually, more often as a group when the magazine is registered. Either way, you receive the same protection. But every short story I’ve sold, nearly one hundred, have all been registered in my name by the publisher.