Many people don't necessarily realise that Hosting and Domain Registration are two separate and distinct services, and while sometimes offered by one company that offers multiple solutions, they are generally kept separate for good reason.
A Domain Registrar is a company who register and hold your domain name. Best known as companies in the UK include such as GoDaddy, 123-REG, UK-REG and 1&1 - the concept is that you pay somewhere from £10 to £30 per year in order for them to 'host' or 'manage' your domain name (i.e. yourcompanyname.com). In return, they process requests when a web user enters your domain address and ensure traffic is directed to the correct place. Such as the website (www.yourcompanyname.com) (A-Record) which would point to the server holding your website files. Or your email (email@example.com) - which would point to the correct email server. (MX Record (MX = Mail Exchange)).
Here at DigitalFlare we recommend 123-REG as they offer a great solution, zero-downtime, and they do not charge to move domains away from them or add bespoke records.
This is the actual server that holds the files that make your website work. (A server is simply a computer which is essentially on 24 hours a day, 365 days a year - its purpose is to serve up files and handle databases etc). There are many aspects to hosting, but essentially a server offers redundant internet connections in order to serve your website to the masses. When you pay for a host, you are paying for the electricity, the internet connection, the physical server hardware and also any software or licensing required which runs on the server.
The domain registrar and the web host really are two totally separate services. One is a place for your domain name to reside; the other is the place for your website's files and emails to reside. Also very important to understand is the fact that you can have two totally different companies handling these different entities - just because you want to move your website hosting to a different company doesn't mean that you have to move your domain name to a new domain registrar at all. In fact, we usually recommend this to our own clients because there are benefits to keeping your domain name and web host totally separate. One instance would be if your website host crashes or suddenly goes out of business. As long as you still have your domain name hosted separately, that account can be accessed and the settings changed in just minutes to point the domain to a new web host ASAP. Some high traffic sites actually rely on a variation of this tactic, having the site replicated on multiple web hosts and managing the domain name settings to direct traffic to the best hosting option at the time according to server loads, etc. For this reason it is very rare that you will see a large website offline, because they handle multiple servers across the globe and switch between servers should one fail.