Web-hosting and domain registration are issues that too often are not very transparent for new site owners when dealing with online services. The question of what your website is called and where it will "live"?, can be crucial to your site's success.
The reality is that both of these services are interconnected though people may elect to handle them separately through different developers or individuals. However it is recommended to handle them together.
Simply stated a domain registration is “the right to use and control” a domain name. Not really related to any content or services associated with that particular domain. The registration process is very simple, consisting mainly of a specific period of time, contact information and potentially some DNS requirements.
Web-hosting on the other hand is a set of services, configuring web-servers to hand out web pages and to handle e-mail for the specified domain. It sounds simple and straight forward but it can be fairly complex depending on the complexity of web-pages in use and filtering for viruses and spam.