There are indeed two different types of cloud hosting. The public clouds are the ones that you use when you are using such web sites as Google Mail or Yahoo, or when you have logged into your Facebook account. They shared the computer servers that are hooked up to that public cloud and experience the benefits of the expanded usability and the associated heightened access to servers that might be all over the world.
The web sites that you put up on the internet through a cloud is placed on that public one that has the ability to keep expanding when you need additional disc space or functionality for some of those complicated scripts that people have a tendency to run. The public cloud, its name taken from the drawings of clouds on diagrams on paper whenever the internet is discussed, has a very important purpose. That is to serve as many web sites as possible and to keep them all on the Internet and functioning properly.