Many people get confused about this so if you are, you are not alone.
A domain name is the web address, such as zagdesign.com or mysite.net. That domain needs to be hosted somewhere.
Websites can be hosted with the same company as hosts your domain but that isn’t required and there could be a slight monetary advantage to do this but not always.
I like picking a domain hosting company with good customer service. I use GoDaddy for domain hosting because they have the great customer service and are inexpensive.
Sites that host your site might also offer you domain hosting. Often that company is not really hosting your domain but they are a qualified reseller of domains.
If your domain is hosted somewhere other than GoDaddy, I am not recommending you run out and switch it. There are several other companies that do a good job.
Here is how it works:
Domain hosted at company X,
Site hosted at company y,
Company X points your domain to Company y.
It gets pretty techie to describe how this works. It is best to allow your Web developer to do this for you. Once it is all set up, you don’t have to worry about it. The set up doesn’t take that long but suffice to say it is easier to do it with some domain hosting companies than others.