Royalty-free images allows businesses license them for a one-time fee and use the licensed images as many times as they like.
The perk of royalty-free images is that there isn’t a need to renew the license for the photo once you’ve purchased it. However, royalty-free doesn’t mean that the buyer has exclusive rights to the image, but that other businesses and individuals may choose to use the image in their work as well.
Copyright-free images are provided by the photographer or owner and can be used by any person, but the ways they can use it are pre-determined by the photographer / owner of the image / picture. Meaning the photographer / owner may still maintain copyright on a particular photo or image and only allow it to be used by any person for non-commercial purposes. They may require anyone who uses their photo or image to credit them each time they get used. Or they may provide authorization for the image to be used by others in any manner they wish — including for commercial purposes.
Public domain images, on the other hand, are creative materials that are not protected by intellectual property laws such as copyright, trademark, or patent laws, and anyone can use a public domain work without obtaining permission, but no one can ever own it.