Suppose you register your domain with one company and host your site with the same business. What happens if the company disappears? Even the big ones can fail.
It actually happened with one of the larger registrars a few years ago, leaving many people and businesses severely inconvenienced. Their websites had disappeared, and they could not access the registrar to point their domain to another company.
Some hosting companies offer a free domain with their package. If you’re new to setting up a website, it may seem an attractive option. But for just $15-20/year (the cost of owning a domain name), it makes more sense to have total control over your domain. After all, it will quickly become an essential asset of your business, carrying with it search engine visibility (“Google juice”), valuable inbound links from other websites, brand awareness and just plain old business goodwill.
If your domain registrar goes down but your website is still standing because it is hosted with a different company, you have time to transfer registration to another registrar. Likewise, If your web host goes down but you can still access your registration, you can find a new web host and point the domain to the new server.
Best practice: register your domain with one company and host your site with another.