Cloud hosting is whereby your website is hosted on a cluster of servers instead of having your site hosted on one server. In case of an issue, your site can be migrated to another server. Based on the cloud computing technology, it allows numerous machines to work in synchrony as one entity. The success of cloud hosting is guaranteed by the presence of many servers.
Shared hosting refers to the hosting plan that has multiple websites hosted together and sharing resources on one server (disk space, storage, bandwidth and databases etc). Most, if not all the web hosting providers offer this hosting plan.