Hosting generally refers to storing data and programs at an off site location. Web hosting for example stores files that are accessible from the Internet.

Like the first person stated Data hosting and Shared hosting are pretty much the same to make things simple. Shared hosting refers to a company that will sell you space on their server for your website. That same server has space that is sold to other website holders also. This is a common practice in Hosting services. Data hosting is really that same thing. The term "data hosting" is really not used. I would suggest you take a look at Heath Hosting. They seem to be the best so far out of all the companies I have delt with. They have excellent service and their support is the best I have had. Check them out!