Domain names are often simply referred to as domains and domain name registrants are frequently referred to as domain owners, although domain name registration with a registrar does not confer any legal ownership of the domain name, only an exclusive right of use for a particular duration of time. The use of domain names in commerce may subject them to trademark law.
If you own a business, your company needs a website. If it doesn't have one, it should. Naturally, online businesses by definition require websites for marketing and selling products or services by definition. In the internet age, however, even local brick-and-mortar business need to at the very least be discoverable via the web (and they probably ought to be selling online, too).
If industry-leading uptime and rapid-scalability are your two biggest concerns, cloud hosting might be just what you're looking for. Cloud hosting will get you access to a cluster of servers from which you can quickly provision resources when you need them. Along with having enough separation from unruly neighbors, your application should be kept safe. VPS and Cloud services are sometimes combined into a hybrid service called Cloud VPS or Scalable VPS.
The server where you bought the domain probably offers hosting services but usually at a cost. If you want to do it for free, have your domain redirected to whatever free web service you decide to use for your website. Remember, free sites are limited in the number of pages and can have a lot of ads. On the other hand, hosting your own website as in Method 2 above, or having your site hosted where you bought and keep the domain, allows you to pretty much create as many pages as you want, without any advertising you don't put up for yourself.
Migration or transfer services are often free or offered at a reasonable fee. These services help move your existing site to the new hosting provider. They can save a huge amount of hassle. Just remember that the migration process is often automated, and may fit in with the host's processes and needs rather than yours. Not everything may migrate, and you may find the organization of the newly migrated site makes for harder maintenance in the long run.