Technically, domain registration and hosting are completely seperate.
Practically, domain registration companies often also provide hosting services, and hosting companies resell domain registration services, so things can get complicated.
This is why this advice is often repeated here:
- Do not get hosting and registration from the same company!
- Make sure that YOU hold the keys (password, registrant name, etc.) to your registrations!
- It's really not a great idea to have hosting in somebody else's name, either.
I assume you hired somebody to handle the technical details of running your web site and/or generating/formatting content, and they made things "convenient" for you, by opening hosting and/or domain registration accounts in their own name.
More like convenient for them when you want to discontinue their services, and they now have you over a barrel.
You probably need to make sure you understand the legal ownership of your content as well. Do you actually own your content, and will you be able to legally take control of it? That's unclear, given your description.
How do you intend to prove that you are the owner of either the domain or the content? Do you have written contracts? Do they clearly state that you are the owner?
Better to have made sure that it was your name on the accounts and that you had access to the logins and passwords...
Would you buy a car, and let the salesman put the title in his own name? Or buy a house and let the real-estate agent, or a remodeling contractor put the title in their name?
Amazingly, people do the equivalent on the Internet every day.